A finite volume method with linearisation in time for the solution of advection-reaction-diffusion systems

The numerical solution in one space dimension of advection--reaction--diffusion systems with nonlinear source terms may invoke a high computational cost when the presently available methods are used. Numerous examples of finite volume schemes with high order spatial discretisations together with various techniques for the approximation of the advection term can be found in the literature. Almost all such techniques result in a nonlinear system of equations as a consequence of the finite volume discretisation especially when there are nonlinear source terms in the associated partial differential equation models. This work introduces a new technique that avoids having such nonlinear systems of equations generated by the spatial discretisation process when nonlinear source terms in the model equations can be expanded in positive powers of the dependent function of interest. The basis of this method is a new linearisation technique for the temporal integration of the nonlinear source terms as a supplementation of a more typical finite volume method. The resulting linear system of equations is shown to be both accurate and significantly faster than methods that necessitate the use of solvers for nonlinear system of equations.

Stability and convergence of an effective numerical method for the time-space fractional Fokker-Planck equation with a nonlinear source term

Fractional Fokker-Planck equations (FFPEs) have gained much interest recently for describing transport dynamics in complex systems that are governed by anomalous diffusion and nonexponential relaxation patterns. However, effective numerical methods and analytic techniques for the FFPE are still in their embryonic state. In this paper, we consider a class of time-space fractional Fokker-Planck equations with a nonlinear source term (TSFFPE-NST), which involve the Caputo time fractional derivative (CTFD) of order α ∈ (0, 1) and the symmetric Riesz space fractional derivative (RSFD) of order μ ∈ (1, 2). Approximating the CTFD and RSFD using the L1-algorithm and shifted Grunwald method, respectively, a computationally effective numerical method is presented to solve the TSFFPE-NST. The stability and convergence of the proposed numerical method are investigated. Finally, numerical experiments are carried out to support the theoretical claims.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.

Membrane associated transporter protein gene (SLC45A2) and the genetic basis of normal human pigmentation variation

This work is concerned with the genetic basis of normal human pigmentation variation. Specifically, the role of polymorphisms within the solute carrier family 45 member 2 (SLC45A2 or membrane associated transporter protein; MATP) gene were investigated with respect to variation in hair, skin and eye colour ― both between and within populations. SLC45A2 is an important regulator of melanin production and mutations in the gene underly the most recently identified form of oculocutaneous albinism. There is evidence to suggest that non-synonymous polymorphisms in SLC45A2 are associated with normal pigmentation variation between populations. Therefore, the underlying hypothesis of this thesis is that polymorphisms in SLC45A2 will alter the function or regulation of the protein, thereby altering the important role it plays in melanogenesis and providing a mechanism for normal pigmentation variation. In order to investigate the role that SLC45A2 polymorphisms play in human pigmentation variation, a DNA database was established which collected pigmentation phenotypic information and blood samples of more than 700 individuals. This database was used as the foundation for two association studies outlined in this thesis, the first of which involved genotyping two previously-described non-synonymous polymorphisms, p.Glu272Lys and p.Phe374Leu, in four different population groups. For both polymorphisms, allele frequencies were significantly different between population groups and the 272Lys and 374Leu alleles were strongly associated with black hair, brown eyes and olive skin colour in Caucasians. This was the first report to show that SLC45A2 polymorphisms were associated with normal human intra-population pigmentation variation. The second association study involved genotyping several SLC45A2 promoter polymorphisms to determine if they also played a role in pigmentation variation. Firstly, the transcription start site (TSS), and hence putative proximal promoter region, was identified using 5' RNA ligase mediated rapid amplification of cDNA ends (RLM-RACE). Two alternate TSSs were identified and the putative promoter region was screened for novel polymorphisms using denaturing high performance liquid chromatography (dHPLC). A novel duplication (c.–1176_–1174dupAAT) was identified along with other previously described single nucleotide polymorphisms (c.–1721C>G and c.–1169G>A). Strong linkage disequilibrium ensured that all three polymorphisms were associated with skin colour such that the –1721G, +dup and –1169A alleles were associated with olive skin in Caucasians. No linkage disequilibrium was observed between the promoter and coding region polymorphisms, suggesting independent effects. The association analyses were complemented with functional data, showing that the –1721G, +dup and –1169A alleles significantly decreased SLC45A2 transcriptional activity. Based on in silico bioinformatic analysis that showed these alleles remove a microphthalmia-associated transcription factor (MITF) binding site, and that MITF is a known regulator of SLC45A2 (Baxter and Pavan, 2002; Du and Fisher, 2002), it was postulated that SLC45A2 promoter polymorphisms could contribute to the regulation of pigmentation by altering MITF binding affinity. Further characterisation of the SLC45A2 promoter was carried out using luciferase reporter assays to determine the transcriptional activity of different regions of the promoter. Five constructs were designed of increasing length and their promoter activity evaluated. Constitutive promoter activity was observed within the first ~200 bp and promoter activity increased as the construct size increased. The functional impact of the –1721G, +dup and –1169A alleles, which removed a MITF consensus binding site, were assessed using electrophoretic mobility shift assays (EMSA) and expression analysis of genotyped melanoblast and melanocyte cell lines. EMSA results confirmed that the promoter polymorphisms affected DNA-protein binding. Interestingly, however, the protein/s involved were not MITF, or at least MITF was not the protein directly binding to the DNA. In an effort to more thoroughly characterise the functional consequences of SLC45A2 promoter polymorphisms, the mRNA expression levels of SLC45A2 and MITF were determined in melanocyte/melanoblast cell lines. Based on SLC45A2’s role in processing and trafficking TYRP1 from the trans-Golgi network to stage 2 melanosmes, the mRNA expression of TYRP1 was also investigated. Expression results suggested a coordinated expression of pigmentation genes. This thesis has substantially contributed to the field of pigmentation by showing that SLC45A2 polymorphisms not only show allele frequency differences between population groups, but also contribute to normal pigmentation variation within a Caucasian population. In addition, promoter polymorphisms have been shown to have functional consequences for SLC45A2 transcription and the expression of other pigmentation genes. Combined, the data presented in this work supports the notion that SLC45A2 is an important contributor to normal pigmentation variation and should be the target of further research to elucidate its role in determining pigmentation phenotypes. Understanding SLC45A2’s function may lead to the development of therapeutic interventions for oculocutaneous albinism and other disorders of pigmentation. It may also help in our understanding of skin cancer susceptibility and evolutionary adaptation to different UV environments, and contribute to the forensic application of pigmentation phenotype prediction.

The genetic basis of human height : the role of estrogen

Height is a complex physical trait that displays strong heritability. Adult height is related to length of the long bones, which is determined by growth at the epiphyseal growth plate. Longitudinal bone growth occurs via the process of endochondral ossification, where bone forms over the differentiating cartilage template at the growth plate. Estrogen plays a major role in regulating longitudinal bone growth and is responsible for inducing the pubertal growth spurt and fusion of the epiphyseal growth plate. However, the mechanism by which estrogen promotes epiphyseal fusion is poorly understood. It has been hypothesised that estrogen functions to regulate growth plate fusion by stimulating chondrocyte apoptosis, angiogenesis and bone cell invasion in the growth plate. Another theory has suggested that estrogen exposure exhausts the proliferative capacity of growth plate chondrocytes, which accelerates the process of chondrocyte senescence, leading to growth plate fusion. The overall objective of this study was to gain a greater understanding of the molecular mechanisms behind estrogen-mediated growth and height attainment by examining gene regulation in chondrocytes and the role of some of these genes in normal height inheritance. With the heritability of height so well established, the initial hypothesis was that genetic variation in candidate genes associated with longitudinal bone growth would be involved in normal adult height variation. The height-related genes FGFR3, CBFA1, ER and CBFA1 were screened for novel polymorphisms using denaturing HPLC and RFLP analysis. In total, 24 polymorphisms were identified. Two SNPs in ER (rs3757323 C>T and rs1801132 G>C) were strongly associated with adult male height and displayed an 8 cm and 9 cm height difference between homozygous genotypes, respectively. The TC haplotype of these SNPs was associated with a 6 cm decrease in height and remarkably, no homozygous carriers of the TC haplotype were identified in tall subjects. No significant associations with height were found for polymorphisms in the FGFR3, CBFA1 or VDR genes. In the epiphyseal growth plate, chondrocyte proliferation, matrix synthesis and chondrocyte hypertrophy are all major contributors to long bone growth. As estrogen plays such a significant role in both growth and final height attainment, another hypothesis of this study was that estrogen exerted its effects in the growth plate by influencing chondrocyte proliferation and mediating the expression of chondrocyte marker genes. The examination of genes regulated by estrogen in chondrocyte-like cells aimed to identify potential regulators of growth plate fusion, which may further elucidate mechanisms involved in the cessation of linear growth. While estrogen did not dramatically alter the proliferation of the SW1353 cell line, gene expression experiments identified several estrogen regulated genes. Sixteen chondrocyte marker genes were examined in response to estrogen concentrations ranging from 10-12 M to 10-8 M over varying time points. Of the genes analysed, IHH, FGFR3, collagen II and collagen X were not readily detectable and PTHrP, GHR, ER, BMP6, SOX9 and TGF1 mRNAs showed no significant response to estrogen treatments. However, the expression of MMP13, CBFA1, BCL-2 and BAX genes were significantly decreased. Interestingly, the majority of estrogen regulated genes in SW1353 cells are expressed in the hypertrophic zone of the growth plate. Estrogen is also known to regulate systemic GH secretion and local GH action. At the molecular level, estrogen functions to inhibit GH action by negatively regulating GH signalling. GH treated SW1353 cells displayed increases in MMP9 mRNA expression (4.4-fold) and MMP13 mRNA expression (64-fold) in SW1353 cells. Increases were also detected in their respective proteins. Treatment with AG490, an established JAK2 inhibitor, blocked the GH mediated stimulation of both MMP9 and MMP13 mRNA expression. The application of estrogen and GH to SW1353 cells attenuated GH-stimulated MMP13 levels, but did not affect MMP9 levels. Investigation of GH signalling revealed that SW1353 cells have high levels of activated JAK2 and exposure to GH, estrogen, AG490 and other signalling inhibitors did not affect JAK2 phosphorylation. Interestingly, AG490 treatment dramatically decreased ERK2 signalling, although GH did stimulate ERK2 phosphorylation above control levels. AG490 also decreased CBFA1 expression, a transcription factor known to activate MMP9 and MMP13. Finally, GH and estrogen treatment increased expression of SOCS3 mRNA, suggesting that SOCS3 may regulate JAK/STAT signalling in SW1353 cells. The modulation of GH-mediated MMP expression by estrogen in SW1353 cells represents a potentially novel mechanism by which estrogen may regulate longitudinal bone growth. However, further investigation is required in order to elucidate the precise mechanisms behind estrogen and GH regulation of MMP13 expression in SW1353 cells. This study has provided additional evidence that estrogen and the ER gene are major factors in the regulation of growth and the determination of adult height. Newly identified polymorphisms in the ER gene not only contribute to our understanding of the genetic basis of human height, but may also be useful in association studies examining other complex traits. This study also identified several estrogen regulated genes and indicated that estrogen modifies the expression of genes which are primarily expressed in the hypertrophic region of the epiphyseal growth plate. Furthermore, synergistic studies incorporating GH and estrogen have revealed the ability of estrogen to attenuate the effects of GH on MMP13 expression, revealing potential pathways by which estrogen may modulate growth plate fusion, longitudinal bone growth and even arthritis.

The Conceptual Basis of Personal Information in Australian Privacy Law

Australian privacy law regulates how government agencies and private sector organisations collect, store and use personal information. A coherent conceptual basis of personal information is an integral requirement of information privacy law as it determines what information is regulated. A 2004 report conducted on behalf of the UK’s Information Commissioner (the 'Booth Report') concluded that there was no coherent definition of personal information currently in operation because different data protection authorities throughout the world conceived the concept of personal information in different ways. The authors adopt the models developed by the Booth Report to examine the conceptual basis of statutory definitions of personal information in Australian privacy laws. Research findings indicate that the definition of personal information is not construed uniformly in Australian privacy laws and that different definitions rely upon different classifications of personal information. A similar situation is evident in a review of relevant case law. Despite this, the authors conclude the article by asserting that a greater jurisprudential discourse is required based on a coherent conceptual framework to ensure the consistent development of Australian privacy law.

Exploring the parameter space of a rabbit ventricular action potential model to investigate the effect of variation on action potential and calcium transients

Computational models for cardiomyocyte action potentials (AP) often make use of a large parameter set. This parameter set can contain some elements that are fitted to experimental data independently of any other element, some elements that are derived concurrently with other elements to match experimental data, and some elements that are derived purely from phenomenological fitting to produce the desired AP output. Furthermore, models can make use of several different data sets, not always derived for the same conditions or even the same species. It is consequently uncertain whether the parameter set for a given model is physiologically accurate. Furthermore, it is only recently that the possibility of degeneracy in parameter values in producing a given simulation output has started to be addressed. In this study, we examine the effects of varying two parameters (the L-type calcium current (I(CaL)) and the delayed rectifier potassium current (I(Ks))) in a computational model of a rabbit ventricular cardiomyocyte AP on both the membrane potential (V(m)) and calcium (Ca(2+)) transient. It will subsequently be determined if there is degeneracy in this model to these parameter values, which will have important implications on the stability of these models to cell-to-cell parameter variation, and also whether the current methodology for generating parameter values is flawed. The accuracy of AP duration (APD) as an indicator of AP shape will also be assessed.

Reduced variance in monozygous twins for multiple MR parameters : implications for disease studies and the genetic basis of brain structure

Twin studies offer the opportunity to determine the relative contribution of genes versus environment in traits of interest. Here, we investigate the extent to which variance in brain structure is reduced in monozygous twins with identical genetic make-up. We investigate whether using twins as compared to a control population reduces variability in a number of common magnetic resonance (MR) structural measures, and we investigate the location of areas under major genetic influences. This is fundamental to understanding the benefit of using twins in studies where structure is the phenotype of interest. Twenty-three pairs of healthy MZ twins were compared to matched control pairs. Volume, T2 and diffusion MR imaging were performed as well as spectroscopy (MRS). Images were compared using (i) global measures of standard deviation and effect size, (ii) voxel-based analysis of similarity and (iii) intra-pair correlation. Global measures indicated a consistent increase in structural similarity in twins. The voxel-based and correlation analyses indicated a widespread pattern of increased similarity in twin pairs, particularly in frontal and temporal regions. The areas of increased similarity were most widespread for the diffusion trace and least widespread for T2. MRS showed consistent reduction in metabolite variation that was significant in the temporal lobe N-acetylaspartate (NAA). This study has shown the distribution and magnitude of reduced variability in brain volume, diffusion, T2 and metabolites in twins. The data suggest that evaluation of twins discordant for disease is indeed a valid way to attribute genetic or environmental influences to observed abnormalities in patients since evidence is provided for the underlying assumption of decreased variability in twins.