Implicit difference approximation for the time fractional diffusion equation

In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order $0<\alpha<1$ ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent with $O(\tau+h^2)$, where $\tau$ and $h$ are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.

Modulation of the SHBG signalling axis

Sex hormone-binding globulin (SHBG) is a homodimeric plasma glycoprotein that is the major sex steroid carrier-protein in the bloodstream and functions also as a key regulator of steroid bioavailability within target tissues, such as the prostate. Additionally, SHBG binds to prostatic cell membranes via the putative and unidentified SHBG receptor (RSHBG), activating a signal transduction pathway implicated in stimulating both proliferation and expression of prostate specific antigen (PSA) in prostate cell lines in vitro. A yeast-two hybrid assay suggested an interaction between SHBG and kallikrein-related protease (KLK) 4, which is a serine protease implicated in the progression of prostate cancer. The potential interaction between these two proteins was investigated in this PhD thesis to determine whether SHBG is a proteolytic substrate of KLK4 and other members of the KLK family including KLK3/PSA, KLK7 and KLK14. Furthermore, the effects from SHBG proteolytic degradation on SHBG-regulated steroid bioavailability and the activation of the putative RSHBG signal transduction pathway were examined in the LNCaP prostate cancer cell line. SHBG was found to be a proteolytic substrate of the trypsin-like KLK4 and KLK14 in vitro, yielding several proteolysis fragments. Both chymotrypsin-like PSA and KLK7 displayed insignificant proteolytic activity against SHBG. The kinetic parameters of SHBG proteolysis by KLK4 and KLK14 demonstrate a strong enzyme-substrate binding capacity, possessing a Km of 1.2 ± 0.7 µM and 2.1 ± 0.6 µM respectively. The catalytic efficiencies (kcat/Km) of KLK4 and KLK14 proteolysis of SHBG were 1.6 x 104 M-1s-1 and 3.8 x 104 M-1s-1 respectively, which were comparable to parameters previously reported for peptide substrates. N-terminal sequencing of the fragments revealed cleavage near the junction of the N- and C-terminal laminin globulin-like (G-like) domains of SHBG, resulting in the division of the two globulins and ultimately the full degradation of these fragments by KLK4 and KLK14 over time. Proteolytic fragments that may retain steroid binding were rapidly degraded by both proteases, while fragments containing residues beyond the steroid binding pocket were less degraded over the same period of time. Degradation of SHBG was inhibited by the divalent metal cations calcium and zinc for KLK4, and calcium, zinc and magnesium for KLK14. The human secreted serine protease inhibitors (serpins), α1-antitrypsin and α2-antiplasmin, inhibited KLK4 and KLK14 proteolysis of SHBG; α1-antichymotrypsin inhibited KLK4 but not KLK14 activity. The inhibition by these serpins was comparable and in some cases more effective than general trypsin protease inhibitors such as aprotinin and phenylmethanesulfonyl fluoride (PMSF). The binding of 5α-dihydrotestosterone (DHT) to SHBG modulated interactions with KLK4 and KLK14. Steroid-free SHBG was more readily digested by both enzymes than DHT-bound SHBG. Moreover, a binding interaction exists between SHBG and pro-KLK4 and pro-KLK14, with DHT strengthening the binding to pro-KLK4 only. The inhibition of androgen uptake by cultured prostate cancer cells, mediated by SHBG steroid-binding, was examined to assess whether SHBG proteolysis by KLK4 and KLK14 modulated this process. Proteolytic digestion eliminated the ability of SHBG to inhibit the uptake of DHT from conditioned media into LNCaP cells. Therefore, the proteolysis of SHBG by KLK4 and KLK14 increased steroid bioavailability in vitro, leading to an increased uptake of androgens by prostate cancer cells. Interestingly, different transcriptional responses of PSA and KLK2, which are androgen-regulated genes, to DHT-bounsd SHBG treatment were observed between low and high passage number LNCaP cells (lpLNCaP and hpLNCaP respectively). HpLNCaP cells treated with DHT-bound SHBG demonstrated a significant synergistic upregulation of PSA and KLK2 above DHT or SHBG treatment alone, which is similar to previously reported downstream responses from RSHBG-mediated signaling activation. As this result was not seen in lpLNCaP cells, only hpLNCaP cells were further investigated to examine the modulation of potential RSHBG activity by KLK4 and KLK14 proteolysis of SHBG. Contrary to reported results, no increase in intracellular cAMP was observed in hpLNCaP cells when treated with SHBG in the presence and absence of either DHT or estradiol. As a result, the modulation of RSHBG-mediated signaling activation could not be determined. Finally, the identification of the RSHBG from both breast (MCF-7) and prostate cancer (LNCaP) cell lines was attempted. Fluorescently labeled peptides corresponding to the putative receptor binding domain (RBD) of SHBG were shown to be internalized by MCF-7 cells. Crosslinking of the RBD peptide to the cell surfaces of both MCF-7 and LNCaP cells, demonstrated the interaction of the peptide with several targets. These targets were then captured using RBD peptides synthesized onto a hydrophilic scaffold and analysed by mass spectrometry. The samples captured by the RBD peptide returned statistically significantly matches for cytokeratin 8, 18 and 19 as well as microtubule-actin crosslinking factor 1, which may indicate a novel interaction between SHBG and these proteins, but ultimately failed to detect a membrane receptor potentially responsible for the putative RSHBG-mediated signaling. This PhD project has reported the proteolytic processing of SHBG by two members of the kallikrein family, KLK4 and KLK14. The effect of SHBG proteolysis by KLK4 and KLK14 on RSHBG-mediated signaling activation was unable to be determined as the reported signal transduction pathway was not activated after treatment with SHBG, in combination with either DHT or estradiol. However, the digestion of SHBG by these two proteases positively regulated androgen bioavailability to prostate cancer cells in vitro. The increased uptake of androgens is deleterious in prostate cancer due to the promotion of proliferation, metastasis, invasion and the inhibition of apoptosis. The increased bioavailability of androgens, from SHBG proteolysis by KLK4 and KLK14, may therefore promote both carcinogenesis and progression of prostate cancer. Finally, this information may contribute to the development of therapeutic treatment strategies for prostate cancer by inhibiting the proteolysis of SHBG, by KLK4 and KLK14, to prevent the increased uptake of androgens by hormone-dependent cancerous tissues.

Algebraic attacks on clock-controlled stream ciphers

Stream ciphers are encryption algorithms used for ensuring the privacy of digital telecommunications. They have been widely used for encrypting military communications, satellite communications, pay TV encryption and for voice encryption of both fixed lined and wireless networks. The current multi year European project eSTREAM, which aims to select stream ciphers suitable for widespread adoptation, reflects the importance of this area of research. Stream ciphers consist of a keystream generator and an output function. Keystream generators produce a sequence that appears to be random, which is combined with the plaintext message using the output function. Most commonly, the output function is binary addition modulo two. Cryptanalysis of these ciphers focuses largely on analysis of the keystream generators and of relationships between the generator and the keystream it produces. Linear feedback shift registers are widely used components in building keystream generators, as the sequences they produce are well understood. Many types of attack have been proposed for breaking various LFSR based stream ciphers. A recent attack type is known as an algebraic attack. Algebraic attacks transform the problem of recovering the key into a problem of solving multivariate system of equations, which eventually recover the internal state bits or the key bits. This type of attack has been shown to be effective on a number of regularly clocked LFSR based stream ciphers. In this thesis, algebraic attacks are extended to a number of well known stream ciphers where at least one LFSR in the system is irregularly clocked. Applying algebriac attacks to these ciphers has only been discussed previously in the open literature for LILI-128. In this thesis, algebraic attacks are first applied to keystream generators using stop-and go clocking. Four ciphers belonging to this group are investigated: the Beth-Piper stop-and-go generator, the alternating step generator, the Gollmann cascade generator and the eSTREAM candidate: the Pomaranch cipher. It is shown that algebraic attacks are very effective on the first three of these ciphers. Although no effective algebraic attack was found for Pomaranch, the algebraic analysis lead to some interesting findings including weaknesses that may be exploited in future attacks. Algebraic attacks are then applied to keystream generators using (p; q) clocking. Two well known examples of such ciphers, the step1/step2 generator and the self decimated generator are investigated. Algebraic attacks are shown to be very powerful attack in recovering the internal state of these generators. A more complex clocking mechanism than either stop-and-go or the (p; q) clocking keystream generators is known as mutual clock control. In mutual clock control generators, the LFSRs control the clocking of each other. Four well known stream ciphers belonging to this group are investigated with respect to algebraic attacks: the Bilateral-stop-and-go generator, A5/1 stream cipher, Alpha 1 stream cipher, and the more recent eSTREAM proposal, the MICKEY stream ciphers. Some theoretical results with regards to the complexity of algebraic attacks on these ciphers are presented. The algebraic analysis of these ciphers showed that generally, it is hard to generate the system of equations required for an algebraic attack on these ciphers. As the algebraic attack could not be applied directly on these ciphers, a different approach was used, namely guessing some bits of the internal state, in order to reduce the degree of the equations. Finally, an algebraic attack on Alpha 1 that requires only 128 bits of keystream to recover the 128 internal state bits is presented. An essential process associated with stream cipher proposals is key initialization. Many recently proposed stream ciphers use an algorithm to initialize the large internal state with a smaller key and possibly publicly known initialization vectors. The effect of key initialization on the performance of algebraic attacks is also investigated in this thesis. The relationships between the two have not been investigated before in the open literature. The investigation is conducted on Trivium and Grain-128, two eSTREAM ciphers. It is shown that the key initialization process has an effect on the success of algebraic attacks, unlike other conventional attacks. In particular, the key initialization process allows an attacker to firstly generate a small number of equations of low degree and then perform an algebraic attack using multiple keystreams. The effect of the number of iterations performed during key initialization is investigated. It is shown that both the number of iterations and the maximum number of initialization vectors to be used with one key should be carefully chosen. Some experimental results on Trivium and Grain-128 are then presented. Finally, the security with respect to algebraic attacks of the well known LILI family of stream ciphers, including the unbroken LILI-II, is investigated. These are irregularly clock- controlled nonlinear filtered generators. While the structure is defined for the LILI family, a particular paramater choice defines a specific instance. Two well known such instances are LILI-128 and LILI-II. The security of these and other instances is investigated to identify which instances are vulnerable to algebraic attacks. The feasibility of recovering the key bits using algebraic attacks is then investigated for both LILI- 128 and LILI-II. Algebraic attacks which recover the internal state with less effort than exhaustive key search are possible for LILI-128 but not for LILI-II. Given the internal state at some point in time, the feasibility of recovering the key bits is also investigated, showing that the parameters used in the key initialization process, if poorly chosen, can lead to a key recovery using algebraic attacks.

The heparan sulfate proteoglycan (HSPG) glypican-3 mediates commitment of MC3T3-E1 cells toward osteogenesis

Heparan sulfate (HS) sugar chains attached to core proteoglycans (PGs) termed HSPGs mediate an extensive range of cell-extracellular matrix (ECM) and growth factor interactions based upon their sulfation patterns. When compared with non-osteogenic (maintenance media) culture conditions, under established osteogenic culture conditions, MC3T3-E1 cells characteristically increase their osteogenic gene expression profile and switch their dominant fibroblast growth factor receptor (FGFR) from FGFR1 (0.5-fold decrease) to FGFR3 (1.5-fold increase). The change in FGFR expression profile of the osteogenic-committed cultures was reflected by their inability to sustain an FGF-2 stimulus, but respond to BMP-2 at day 14 of culture. The osteogenic cultures decreased their chondroitin and dermatan sulfate PGs (biglycan, decorin, and versican), but increased levels of the HS core protein gene expression, in particular glypican-3. Commitment and progress through osteogenesis is accompanied by changes in FGFR expression, decreased GAG initiation but increased N- and O-sulfation and reduced remodeling of the ECM (decreased heparanase expression) resulting in the production of homogenous (21 kDa) HS chain. With the HSPG glypican-3 expression strongly upregulated in these processes, siRNA was used to knockdown this gene to examine the effect on osteogenic commitment. Reduced glypican-3 abrogated the expression of Runx2, and thus differentiation. The reintroduction of this HSPG into Runx2-null cells allowed osteogenesis to proceed. These results demonstrate the dependence of osteogenesis on specific HS chains, in particular those associated with glypican-3.

Synergism between Wnt3a and heparin enhances osteogenesis via a phosphoinositide 3-kinase/Akt/RUNX2 pathway

A new strategy has emerged to improve healing of bone defects using exogenous glycosaminoglycans by increasing the effectiveness of bone-anabolic growth factors. Wnt ligands play an important role in bone formation. However, their functional interactions with heparan sulfate/heparin have only been investigated in non-osseous tissues. Our study now shows that the osteogenic activity of Wnt3a is cooperatively stimulated through physical interactions with exogenous heparin. N-Sulfation and to a lesser extent O-sulfation of heparin contribute to the physical binding and optimal co-stimulation of Wnt3a. Wnt3a-heparin signaling synergistically increases osteoblast differentiation with minimal effects on cell proliferation. Thus, heparin selectively reduces the effective dose of Wnt3a needed to elicit osteogenic, but not mitogenic responses. Mechanistically, Wnt3a-heparin signaling strongly activates the phosphoinositide 3-kinase/Akt pathway and requires the bone-related transcription factor RUNX2 to stimulate alkaline phosphatase activity, which parallels canonical beta-catenin signaling. Collectively, our findings establish the osteo-inductive potential of a heparin-mediated Wnt3a-phosphoinositide 3-kinase/Akt-RUNX2 signaling network and suggest that heparan sulfate supplementation may selectively reduce the therapeutic doses of peptide factors required to promote bone formation.

The osteogenic transcription factor Runx2 regulates components of the fibroblast growth factor/proteoglycan signaling axis in osteoblasts

Heparan sulfate proteoglycans cooperate with basic fibroblast growth factor (bFGF/FGF2) signaling to control osteoblast growth and differentiation, as well as metabolic functions of osteoblasts. FGF2 signaling modulates the expression and activity of Runt-related transcription factor 2 (Runx2/Cbfa1), a key regulator of osteoblast proliferation and maturation. Here, we have characterized novel Runx2 target genes in osteoprogenitors under conditions that promote growth arrest while not yet permitting sustained phenotypic maturation. Runx2 enhances expression of genes related to proteoglycan-mediated signaling, including FGF receptors (e.g., FGFR2 and FGFR3) and proteoglycans (e.g., syndecans [Sdc1, Sdc2, Sdc3], glypicans [Gpc1], versican [Vcan]). Runx2 increases expression of the glycosyltransferase Exostosin-1 (Ext1) and heparanase, as well as alters the relative expression of N-linked sulfotransferases (Ndst1 = Ndst2 > Ndst3) and enzymes mediating O-linked sulfation of heparan sulfate (Hs2st > Hs6st) or chondroitin sulfate (Cs4st > Cs6st). Runx2 cooperates with FGF2 to induce expression of Sdc4 and the sulfatase Galns, but Runx2 and FGF2 suppress Gpc6, thus suggesting intricate Runx2 and FGF2 dependent changes in proteoglycan utilization. One functional consequence of Runx2 mediated modulations in proteoglycan-related gene expression is a change in the responsiveness of bone markers to FGF2 stimulation. Runx2 and FGF2 synergistically enhance osteopontin expression (>100 fold), while FGF2 blocks Runx2 induction of alkaline phosphatase. Our data suggest that Runx2 and the FGF/proteoglycan axis may form an extracellular matrix (ECM)-related regulatory feed-back loop that controls osteoblast proliferation and execution of the osteogenic program.

Nephrotoxicity and nephrocarcinogenicity of dinitrotoluene : new aspects to be considered

Technical dinitrotoluene (DNT) is a mixture of 2,4- and 2,6-DNT. In humans, industrial or environmental exposure can occur orally, by inhalation, or by skin contact. The classification of DNT as an 'animal carcinogen' is based on the formation of malignant tumors in kidneys, liver, and mammary glands of rats and mice. Clear signs of toxic nephropathy were found in rats dosed with DNT, and the concept was derived of an interrelation between renal toxicity and carcinogenicity. Recent data point to the carcinogenicity of DNT on the urinary tract of exposed humans. Between 1984 and 1997, 6 cases of urothelial cancer and 14 cases of renal cell cancer were diagnosed in a group of 500 underground mining workers in the copper mining industry of the former GDR and having high exposures to explosives containing technical DNT. The incidences of both urothelial and renal cell tumors in this group were 4.5 and 14.3 times higher, respectively, than anticipated on the basis of the cancer registers of the GDR. The genotyping of all identified tumor patients for the polymorphic enzymes NAT2, GSTM1, and GSTT1 identified the urothelial tumor cases as exclusively 'slow acetylates'. A group of 161 miners highly exposed to DNT was investigated for signs of subclinical renal damage. The exposures were categorized semi-quantitatively into 'low', 'medium', 'high', and 'very high'. A straight dose-dependence of the excretion of urinary biomarker proteins with the ranking of exposure was seen. Biomarker excretion (alpha1-microglobulin, glutathione S-transferases alpha and pi) indicated that DNT-induced damage was directed toward the tubular system. New data on DNT-exposed humans appear consistent with the concept of cancer initiation by DNT isomers and the subsequent promotion of renal carcinogenesis by selective damage to the proximal tubule. The differential pathways of metabolic activation of DNT appear to apply to the proximal tubule of the kidney and to the urothelium of the renal pelvis and lower urinary tract as target tissues of carcinogenicity.

Pathological excretion patterns of urinary proteins in miners highly exposed to dinitrotoluene

A cohort of 161 underground miners who had been highly exposed to dinitrotoluene (DNT) in the copper-mining industry of the former German Democratic Republic was reinvestigated for signs of subclinical renal damage. The study included a screening of urinary proteins excreted by sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE), and quantitations of the specific urinary proteins α 1-microglobulin and glutathione-S-transferase α (GST α) as biomarkers for damage of the proximal tubule and glutathione-S-transferase π (GST π) for damage of the distal tubule. The exposures were categorized semiquantitatively (low, medium, high, and very high), according to the type and duration of professional contact with DNT. A straight dose-dependence of pathological protein excretion patterns with the semiquantitative ranking of DNT exposure was seen. Most of the previously reported cancer cases of the urinary tract, especially those in the higher exposed groups, were confined to pathological urinary protein excretion patterns. The damage from DNT was directed toward the tubular system. In many cases, the appearance of Tamm-Horsfall protein, a 105-kD protein marker, was noted. Data on the biomarkers α 1-microglobulin, GST α, and GST π consistently demonstrated a dose-dependent increase in tubular damage, which confirmed the results of screening by SDS-PAGE and clearly indicated a nephrotoxic effect of DNT under the given conditions of exposure. Within the cluster of cancer patients observed among the DNT-exposed workers, only in exceptional cases were normal biomarker excretions found.

Non-major-histocompatibility-complex genetics of ankylosing spondylitis

There is strong evidence from twin and family studies indicating that a substantial proportion of the heritability of susceptibility to ankylosing spondylitis (AS) and its clinical manifestations is encoded by non-major-histocompatibility-complex genes. Efforts to identify these genes have included genomewide linkage studies and candidate gene association studies. One region, the interleukin (IL)-1 gene complex on chromosome 2, has been repeatedly associated with AS in both Caucasians and Asians. It is likely that more than one gene in this complex is involved in AS, with the strongest evidence to date implicating IL-1A. Identifying the genes underlying other linkage regions has been difficult due to the lack of obvious candidates and the low power of most studies to date to identify genes of the small to moderate magnitude that are likely to be involved. The field is moving towards genomewide association analysis, involving much larger datasets of unrelated cases and controls. Early successes using this approach in other diseases indicates that it is likely to identify genes in common diseases like AS, but there remains the risk that the common-variant, common-disease hypothesis will not hold true in AS. Nonetheless, it is appropriate for the field to be cautiously optimistic that the next few years will bring great advances in our understanding of the genetics of this condition.

Long-term growth and anthropometry after childhood liver transplantation

Objectives: To describe longitudinal height, weight, and body mass index changes up to 15 years after childhood liver transplantation. Study design: Retrospective chart review of patients who underwent liver transplant from 1985-2004 was performed. Subjects were age <18 years at transplant, survived ≥5 years, with at least 2 recorded measurements, of which one was ≥5 years post-transplant. Measurements were recorded pre-transplant, 1, 5, 10, and 15 years later. Results: Height and weight data were available in 98 and 104 patients, respectively; 47% were age <2 years at transplant; 58% were Australian, and the rest were from Japan. Height recovery continued for at least 10 years to reach the 26th percentile (Z-score -0.67) 15 years after transplant. Australians had better growth recovery and attained 47th percentile (Z-score -0.06) at 15 years. Weight recovery was most marked in the first year and continued for 15 years even in well-nourished children. Growth impaired and malnourished children at transplant exhibited the best growth, but remained significantly shorter and lighter even 15 years later. No effect of sex or age at transplant was noted on height or weight recovery. Post-transplant factors significantly impact growth recovery and likely caused the dichotomous growth recovery between Australian and Japanese children; 9% (9/98) of patients were overweight on body mass index calculations at 10-15 years but none were obese. Conclusions: After liver transplant, children can expect ongoing height and weight recovery for at least 10-15 years. Growth impairment at transplant and post-transplant care significantly impact long-term growth recovery. Copyright © 2013 Mosby Inc. All rights reserved.

Association study of the calcitonin gene-related polypeptide-alpha (CALCA) and the receptor activity modifying 1 (RAMP1) genes with migraine

Migraine is a common neurovascular brain disorder characterised by recurrent attacks of severe headache that may be accompanied by various neurological symptoms. Migraine is thought to result from activation of the trigeminovascular system followed by vasodilation of pain-producing intracranial blood vessels and activation of second-order sensory neurons in the trigeminal nucleus caudalis. Calcitonin gene-related peptide (CGRP) is a mediator of neurogenic inflammation and the most powerful vasodilating neuropeptide, and has been implicated in migraine pathophysiology. Consequently, genes involved in CGRP synthesis or CGRP receptor genes may play a role in migraine and/or increase susceptibility. This study investigates whether variants in the gene that encodes CGRP, calcitonin-related polypeptide alpha (CALCA) or in the gene that encodes a component of its receptor, receptor activity modifying protein 1 (RAMP1), are associated with migraine pathogenesis and susceptibility. The single nucleotide polymorphisms (SNPs) rs3781719 and rs145837941 in the CALCA gene, and rs3754701 and rs7590387 at the RAMP1 locus, were analysed in an Australian Caucasian population of migraineurs and matched controls. Although we find no significant association of any of the SNPs tested with migraine overall, we detected a nominally significant association (p = 0.031) of the RAMP1 rs3754701 variant in male migraine subjects, although this is non-significant after Bonferroni correction for multiple testing.