Some Remarks on the Approximation of Transitional Density in Stochastic Differential Equations

Aijt-Sahalia (2002) introduced a method to estimate transitional probability densities of di®usion processes by means of Hermite expansions with coe±cients determined by means of Taylor series. This note describes a numerical procedure to ¯nd these coe±cients based on the calculation of moments. One advantage of this procedure is that it can be used e®ectively when the mathematical operations required to ¯nd closed-form expressions for these coe±cients are otherwise infeasible.

Relative entropy rate based multiple hidden Markov Model Approximation

This paper proposes a novel relative entropy rate (RER) based approach for multiple HMM (MHMM) approximation of a class of discrete-time uncertain processes. Under different uncertainty assumptions, the model design problem is posed either as a min-max optimisation problem or stochastic minimisation problem on the RER between joint laws describing the state and output processes (rather than the more usual RER between output processes). A suitable filter is proposed for which performance results are established which bound conditional mean estimation performance and show that estimation performance improves as the RER is reduced. These filter consistency and convergence bounds are the first results characterising multiple HMM approximation performance and suggest that joint RER concepts provide a useful model selection criteria. The proposed model design process and MHMM filter are demonstrated on an important image processing dim-target detection problem.

A surface plasmon resonance-based solution affinity assay for heparan sulfate-binding proteins

A surface plasmon resonance-based solution affinity assay is described for measuring the Kd of binding of heparin/heparan sulfate-binding proteins with a variety of ligands. The assay involves the passage of a pre-equilibrated solution of protein and ligand over a sensor chip onto which heparin has been immobilised. Heparin sensor chips prepared by four different methods, including biotin–streptavidin affinity capture and direct covalent attachment to the chip surface, were successfully used in the assay and gave similar Kd values. The assay is applicable to a wide variety of heparin/HS-binding proteins of diverse structure and function (e.g., FGF-1, FGF-2, VEGF, IL-8, MCP-2, ATIII, PF4) and to ligands of varying molecular weight and degree of sulfation (e.g., heparin, PI-88, sucrose octasulfate, naphthalene trisulfonate) and is thus well suited for the rapid screening of ligands in drug discovery applications.

Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation

In this paper, we consider the variable-order nonlinear fractional diffusion equation View the MathML source where xRα(x,t) is a generalized Riesz fractional derivative of variable order View the MathML source and the nonlinear reaction term f(u,x,t) satisfies the Lipschitz condition |f(u1,x,t)-f(u2,x,t)|less-than-or-equals, slantL|u1-u2|. A new explicit finite-difference approximation is introduced. The convergence and stability of this approximation are proved. Finally, some numerical examples are provided to show that this method is computationally efficient. The proposed method and techniques are applicable to other variable-order nonlinear fractional differential equations.

Recombinant protein production using a Tobacco yellow dwarf virus-based episomal expression vector : control of Rep activity

Over the past decade, plants have been used as expression hosts for the production of pharmaceutically important and commercially valuable proteins. Plants offer many advantages over other expression systems such as lower production costs, rapid scale up of production, similar post-translational modification as animals and the low likelihood of contamination with animal pathogens, microbial toxins or oncogenic sequences. However, improving recombinant protein yield remains one of the greatest challenges to molecular farming. In-Plant Activation (InPAct) is a newly developed technology that offers activatable and high-level expression of heterologous proteins in plants. InPAct vectors contain the geminivirus cis elements essential for rolling circle replication (RCR) and are arranged such that the gene of interest is only expressed in the presence of the cognate viral replication-associated protein (Rep). The expression of Rep in planta may be controlled by a tissue-specific, developmentally regulated or chemically inducible promoter such that heterologous protein accumulation can be spatially and temporally controlled. One of the challenges for the successful exploitation of InPAct technology is the control of Rep expression as even very low levels of this protein can reduce transformation efficiency, cause abnormal phenotypes and premature activation of the InPAct vector in regenerated plants. Tight regulation over transgene expression is also essential if expressing cytotoxic products. Unfortunately, many tissue-specific and inducible promoters are unsuitable for controlling expression of Rep due to low basal activity in the absence of inducer or in tissues other than the target tissue. This PhD aimed to control Rep activity through the production of single chain variable fragments (scFvs) specific to the motif III of Tobacco yellow dwarf virus (TbYDV) Rep. Due to the important role played by the conserved motif III in the RCR, it was postulated that such scFvs can be used to neutralise the activity of the low amount of Rep expressed from a “leaky” inducible promoter, thus preventing activation of the TbYDV-based InPAct vector until intentional induction. Such scFvs could also offer the potential to confer partial or complete resistance to TbYDV, and possibly heterologous viruses as motif III is conserved between geminiviruses. Studies were first undertaken to determine the levels of TbYDV Rep and TbYDV replication-associated protein A (RepA) required for optimal transgene expression from a TbYDV-based InPAct vector. Transient assays in a non-regenerable Nicotiana tabacum (NT-1) cell line were undertaken using a TbYDV-based InPAct vector containing the uidA reporter gene (encoding GUS) in combination with TbYDV Rep and RepA under the control of promoters with high (CaMV 35S) or low (Banana bunchy top virus DNA-R, BT1) activity. The replication enhancer protein of Tomato leaf curl begomovirus (ToLCV), REn, was also used in some co-bombardment experiments to examine whether RepA could be substituted by a replication enhancer from another geminivirus genus. GUS expression was observed both quantitatively and qualitatively by fluorometric and histochemical assays, respectively. GUS expression from the TbYDV-based InPAct vector was found to be greater when Rep was expected to be expressed at low levels (BT1 promoter) rather than high levels (35S promoter). GUS expression was further enhanced when Rep and RepA were co-bombarded with a low ratio of Rep to RepA. Substituting TbYDV RepA with ToLCV REn also enhanced GUS expression but more importantly highest GUS expression was observed when cells were co-transformed with expression vectors directing low levels of Rep and high levels of RepA irrespective of the level of REn. In this case, GUS expression was approximately 74-fold higher than that from a non-replicating vector. The use of different terminators, namely CaMV 35S and Nos terminators, in InPAct vectors was found to influence GUS expression. In the presence of Rep, GUS expression was greater using pInPActGUS-Nos rather than pInPActGUS-35S. The only instance of GUS expression being greater from vectors containing the 35S terminator was when comparing expression from cells transformed with Rep, RepA and REnexpressing vectors and either non-replicating vectors, p35SGS-Nos or p35SGS-35S. This difference was most likely caused by an interaction of viral replication proteins with each other and the terminators. These results indicated that (i) the level of replication associated proteins is critical to high transgene expression, (ii) the choice of terminator within the InPAct vector may affect expression levels and (iii) very low levels of Rep can activate InPAct vectors hence controlling its activity is critical. Prior to generating recombinant scFvs, a recombinant TbYDV Rep was produced in E. coli to act as a control to enable the screening for Rep-specific antibodies. A bacterial expression vector was constructed to express recombinant TbYDV Rep with an Nterminal His-tag (N-His-Rep). Despite investigating several purification techniques including Ni-NTA, anion exchange, hydrophobic interaction and size exclusion chromatography, N-His-Rep could only be partially purified using a Ni-NTA column under native conditions. Although it was not certain that this recombinant N-His-Rep had the same conformation as the native TbYDV Rep and was functional, results from an electromobility shift assay (EMSA) showed that N-His-Rep was able to interact with the TbYDV LIR and was, therefore, possibly functional. Two hybridoma cell lines from mice, immunised with a synthetic peptide containing the TbYDV Rep motif III amino acid sequence, were generated by GenScript (USA). Monoclonal antibodies secreted by the two hybridoma cell lines were first screened against denatured N-His-Rep in Western analysis. After demonstrating their ability to bind N-His-Rep, two scFvs (scFv1 and scFv2) were generated using a PCR-based approach. Whereas the variable heavy chain (VH) from both cell lines could be amplified, only the variable light chain (VL) from cell line 2 was amplified. As a result, scFv1 contained VH and VL from cell line 1, whereas scFv2 contained VH from cell line 2 and VL from cell line 1. Both scFvs were first expressed in E. coli in order to evaluate their affinity to the recombinant TbYDV N-His-Rep. The preliminary results demonstrated that both scFvs were able to bind to the denatured N-His-Rep. However, EMSAs revealed that only scFv2 was able to bind to native N-His-Rep and prevent it from interacting with the TbYDV LIR. Each scFv was cloned into plant expression vectors and co-bombarded into NT-1 cells with the TbYDV-based InPAct GUS expression vector and pBT1-Rep to examine whether the scFvs could prevent Rep from mediating RCR. Although it was expected that the addition of the scFvs would result in decreased GUS expression, GUS expression was found to slightly increase. This increase was even more pronounced when the scFvs were targeted to the cell nucleus by the inclusion of the Simian virus 40 large T antigen (SV40) nuclear localisation signal (NLS). It was postulated that the scFvs were binding to a proportion of Rep, leaving a small amount available to mediate RCR. The outcomes of this project provide evidence that very high levels of recombinant protein can theoretically be expressed using InPAct vectors with judicious selection and control of viral replication proteins. However, the question of whether the scFvs generated in this project have sufficient affinity for TbYDV Rep to prevent its activity in a stably transformed plant remains unknown. It may be that other scFvs with different combinations of VH and VL may have greater affinity for TbYDV Rep. Such scFvs, when expressed at high levels in planta, might also confer resistance to TbYDV and possibly heterologous geminiviruses.

A study of water binding, mobility and dehydration in contact lens hydrogels using NMR

Hydrogel polymers are used for the manufacture of soft (or disposable) contact lenses worldwide today, but have a tendency to dehydrate on the eye. In vitro methods that can probe the potential for a given hydrogel polymer to dehydrate in vivo are much sought after. Nuclear magnetic resonance (NMR) has been shown to be effective in characterising water mobility and binding in similar systems (Barbieri, Quaglia et al., 1998, Larsen, Huff et al., 1990, Peschier, Bouwstra et al., 1993), predominantly through measurement of the spin-lattice relaxation time (T1), the spinspin relaxation time (T2) and the water diffusion coefficient (D). The aim of this work was to use NMR to quantify the molecular behaviour of water in a series of commercially available contact lens hydrogels, and relate these measurements to the binding and mobility of the water, and ultimately the potential for the hydrogel to dehydrate. As a preliminary study, in vitro evaporation rates were measured for a set of commercial contact lens hydrogels. Following this, comprehensive measurement of the temperature and water content dependencies of T1, T2 and D was performed for a series of commercial hydrogels that spanned the spectrum of equilibrium water content (EWC) and common compositions of contact lenses that are manufactured today. To quantify material differences, the data were then modelled based on theory that had been used for similar systems in the literature (Walker, Balmer et al., 1989, Hills, Takacs et al., 1989). The differences were related to differences in water binding and mobility. The evaporative results suggested that the EWC of the material was important in determining a material's potential to dehydrate in this way. Similarly, the NMR water self-diffusion coefficient was also found to be largely (if not wholly) determined by the WC. A specific binding model confirmed that the we was the dominant factor in determining the diffusive behaviour, but also suggested that subtle differences existed between the materials used, based on their equilibrium we (EWC). However, an alternative modified free volume model suggested that only the current water content of the material was important in determining the diffusive behaviour, and not the equilibrium water content. It was shown that T2 relaxation was dominated by chemical exchange between water and exchangeable polymer protons for materials that contained exchangeable polymer protons. The data was analysed using a proton exchange model, and the results were again reasonably correlated with EWC. Specifically, it was found that the average water mobility increased with increasing EWe approaching that of free water. The T1 relaxation was also shown to be reasonably well described by the same model. The main conclusion that can be drawn from this work is that the hydrogel EWe is an important parameter, which largely determines the behaviour of water in the gel. Higher EWe results in a hydrogel with water that behaves more like bulk water on average, or is less strongly 'bound' on average, compared with a lower EWe material. Based on the set of materials used, significant differences due to composition (for materials of the same or similar water content) could not be found. Similar studies could be used in the future to highlight hydrogels that deviate significantly from this 'average' behaviour, and may therefore have the least/greatest potential to dehydrate on the eye.

The expression of ADAM-9 and -10 in prostate cancer and their regulation by dihydrotestosterone, insulin-like growth Factor-1 and epidermal growth factor

Prostrate Cancer(PCa)is the most common cause of cancer death amongst Western males. PCa occurs in two distinct stages. In its early stage, growth and development is dependent primarily on male sex hormones (androgens) such as testosterone, although other growth factors have roles maintaining PCa cell survival in this stage. In the later stage of PCa development, growth and.maintenance is independent of androgen stimulation and growth factors including Insulin-like Growth Factor -1 (IGf.:·l) and Epidermal Growth Factor (EGF) are thought to have more crucial roles in cell survival and PCa progression. PCa, in its late stages, is highly aggressive and metastatic, that is, tumorigenic cells migrate from the primary site of the body (prostate) and travel via the systemic and lymphatic circulation, residing and colonising in the bone, lymph node, lung, and in more rare cases, the brain. Metastasis involves both cell migration and tissue degradation activities. The degradation of the extracellular matrix (ECM), the tissue surrounding the organ, is mediated in part by members of a family of 26 proteins called the Matrix Metalloproteases (MMPs), whilst ceil adhesion molecules, of which proteins known as Integrins are included, mediate ce11 migration. A family of proteins known as the ADAMs (A Disintegrin . And Metalloprotease domain) were a recently characterised family at the commencement of this study and now comprise 34 members. Because of their dual nature, possessing an active metaiioprotease domain, homologous to that of the MMPs, and an integrin-binding domain capable of regulating cell-cell and cell-ECM contacts, it was thought likely that members of the ADAMs family may have implications for the progression of aggressive cancers such as those ofthe prostate. This study focussed on two particular ADAMs -9 and -10. ADAM-9 has an active metalloprotease domain, which has been shown to degrade constituents of the ECM, including fibronectin, in vitro. It also has an integrin-binding capacity through association with key integrins involved in PCa progression, such as a6~1. ADAM-10 has no such integrin binding activities, but its bovine orthologue, MADM, is able to degrade coHagen type IV, a major component of basement membranes. It is likely human ADAM-10 has the same activity. It is also known to cleave Ll -a protein involved in cell anchorage activities - and collagen type XVII - which is a principal component of the hemidesmosomes of cellular tight junctions. The cleavage of these proteins enables the cell to be released from the surrounding environment and commence migratory activities, as required in metastasis. Previous studies in this laboratory showed the mRNA expression of the five ADAMs -9,- 10, -11, -15 and -17 in PCa cell lines, characteristic of androgen-dependent and androgen independent disease. These studies were furthered by the characterisation of AD AM-9, -10 and -17 mRNA regulation by Dihydrotestosterone (DHT) in the androgen-responsive cell line (LNCaP). ADAM-9 and -10 mRNA levels were elevated in response to DHT stimulation. Further to these observations, the expression of ADAM-9 and -10 was shown in primary prostate biopsies from patients with PCa. ADAM-1 0 was expressed in the cytoplasm and on the ceH membrane in epithelial and basal cells ofbenign prostate glands, but in high-grade PCa glands, ADAM-I 0 expression was localised to the nucleus and its expression levels appeared to be elevated when compared to low-grade PCa glands. These studies provided a strong background for the hypothesis that ADAM-9 and -10 have key roles in the development ofPCa and provided a basis for further studies.The aims of this study were to: 1) characterise the expression, localisation and levels, of ADAM-9 and -10 mRNA and protein in cell models representing characteristics of normal through androgen-dependent to androgen-independent PCa, as well as to expand the primary PCa biopsy data for ADAM-9 and ADAM-10 to encompass PCa bone metastases 2) establish an in vitro cell system, which could express elevated levels of ADAM-1 0 so that functional cell-based assays such as cell migration, invasion and attachment could be carried out, and 3) to extend the previous hormonal regulation data, to fully characterise the response of ADAM-9 and -10 mRNA and protein levels to DHT, IGF-1, DHT plus IGF-1 and EGF in the hormonal/growth factor responsive cell line LNCaP. For aim 1 (expression of ADAM-9 and -10 mRNA and protein), ADAM-9 and -10 mRNA were characterised by R T -PCR, while their protein products were analysed by Western blot. Both ADAM-9 and -10 mRNA and protein were expressed at readily detectable levels across progressively metastatic PCa cell lines model that represent characteristics of low-grade,. androgen-dependent (LNCaP and C4) to high-grade, androgen-independent (C4-2 and C4-2B) PCa. When the non-tumorigenic prostate cell line RWPE-1 was compared with the metastatic PCa cell line PC-3, differential expression patterns were seen by Western blot analysis. For ADAM-9, the active form was expressed at higher levels in RWPE-1, whilst subcellular fractionation showed that the active form of ADAM-9 was predominantly located in the cell nucleus. For ADAM-I 0, in both of the cell Jines, a nuclear specific isoform of the mature, catalytically active ADAM-I 0 was found. This isoforrn differed by -2 kDa in Mr (smaller) than the cytoplasmic specific isoform. Unprocessed ADAM-I 0 was readily detected in R WPE-1 cell lines but only occasionally detected in PC-3 cell lines. Immunocytochemistry using ADAM-9 and -10 specific antibodies confirmed nuclear, cytoplasmic and membrane expression of both ADAMs in these two cell lines. To examine the possibility of ADAM-9 and -10 being shed into the extracellular environment, membrane vesicles that are constitutively shed from the cell surface and contain membrane-associated proteins were collected from the media of the prostate cell lines RWPE-1, LNCaP and PC-3. ADAM-9 was readily detectable in RWPE- 1 and LNCaP cell membrane vesicles by Western blot analysis, but not in PC-3 cells, whilst the expression of ADAM-I 0 was detected in shed vesicles from each of these prostate cell lines. By Laser Capture Microdissection (LCM), secretory epithelial cells of primary prostate gland biopsies were isolated from benign and malignant glands. These secretory cells, by Western blot analysis, expressed similar Mr bands for ADAM-9 and -10 that were found in PCa cell lines in vitro, indicating that the nuclear specific isoforrn of ADAM-I 0 was present in PCa primary tumours and may represent the predominantly nuclear form of ADAM-I 0 expression, previously shown in high-grade PCa by immunohistochemistry (IHC). ADAM-9 and -10 were also examined by IHC in bone metastases taken from PCa patients at biopsy. Both ADAMs could be detected at levels similar to those shown for Prostate Specific Antigen (PSA) in these biopsies. Furthermore, both ADAM-9 and -10 were predominantly membrane- bound with occasional nuclear expression. For aim 2, to establish a cell system that over-expressed levels of ADAM-10, two fulllength ADAM-I 0 mammalian expression vectors were constructed; ADAM-I 0 was cloned into pcDNA3.1, which contains a CMV promoter, and into pMEP4, containing an inducible metallothionine promoter, whose activity is stimulated by the addition of CdC}z. The efficiency of these two constructs was tested by way of transient transfection in the PCa cell line PC-3, whilst the pcDNA3.1 construct was also tested in the RWPE-1 prostate cell line. Resultant Western blot analysis for all transient transfection assays showed that levels of ADAM-I 0 were not significantly elevated in any case, when compared to levels of the housekeeping gene ~-Tubulin, despite testing various levels of vector DNA, and, for pMEP4, the induction of the transfected cell system with different degrees of stimulation with CdCh to activate the metallothionine promoter post-transfection. Another study in this laboratory found similar results when the same full length ADAM-10 sequence was cloned into a Green Fluorescent Protein (GFP) expressing vector, as no fluorescence was observed by means of transient tran sfection in the same, and other, PCa cell lines. It was hypothesised that the Kozak sequence included in the full-length construct (human ADAMI 0 naturally occurring sequence) is not strong enough to initiate translation in an artificial system, in cells, which, as described in Aim 1, are already expressing readily detectable levels of endogenous ADAM-10. As a result, time constraints prevented any further progress with Aim 2 and functional studies including cell attachment, invasion and migration were unable to be explored. For Aim 3, to characterise the response of ADAM-9 and -10 mRNA and protein levels to DHT, IGF-1, DHT plus IGF-1 and EGF in LNCaP cells, the levels of ADAM-9 and -10 mRNA were not stimulated by DHT or IGF-I alone, despite our previous observations that initially characterised ADAM-9 and -10 mRNA as being responsive to DHT. However, IGF-1 in synergy with DHT did significantly elevate mRNA levels ofboth ADAMs. In the case of ADAM-9 and -10 protein, the same trends of stimulation as found at the rnRNA level were shown by Western blot analysis when ADAM-9 and -10 signal intensity was normalised with the housekeeping protein ~-Tubulin. For EGF treatment, both ADAM-9 and -10 mRNA and protein levels were significantly elevated, and further investigation vm found this to be the case for each of these ADAMs proteins in the nuclear fractions of LNCaP cells. These studies are the first to describe extensively, the expression and hormonal/growth factor regulation of two members of the ADAMs family ( -9 and -1 0) in PCa. These observations imply that the expression of ADAM-9 and -10 have varied roles in PCa whilst it develops from androgen-sensitive (early stage disease), through to an androgeninsensitive (late-stage), metastatic disease. Further studies are now required to investigate the several key areas of focus that this research has revealed, including: • Investigation of the cellular mechanisms that are involved in actively transporting the ADAMs to the cell's nuclear compartment and the ADAMs functional roles in the cell nucleus. • The construction of a full-length human ADAM-10 mammalian expression construct with the introduction of a new Kozak sequence, that elevates ADAM-I 0 expression in an in vitro cell system are required, so that functional assays such as cell invasion, migration and attachment may be carried out to fmd the functional consequences of ADAM expression on cellular behaviour. • The regulation studies also need to be extended by confirming the preliminary observations that the nuclear levels of ADAMs may also be elevated by hormones and growth factors such as DHT, IGF-1 and EGF, as well as the regulation of levels of plasma membrany vesicle associated ADAM expression. Given the data presented in this study, it is likely the ADAMs have differential roles throughout the development of PCa due to their differential cellular localisation and synergistic growth-factor regulation. These observations, along with those further studies outlined above, are necessary in identifying these specific components ofPCa metastasis to which the ADAMs may contribute.