A Crank--Nicolson ADI spectral method for a two-dimensional riesz space fractional nonlinear reaction-diffusion equation

In this paper, a new alternating direction implicit Galerkin--Legendre spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed. The temporal component is discretized by the Crank--Nicolson method. The detailed implementation of the method is presented. The stability and convergence analysis is strictly proven, which shows that the derived method is stable and convergent of order $2$ in time. An optimal error estimate in space is also obtained by introducing a new orthogonal projector. The present method is extended to solve the fractional FitzHugh--Nagumo model. Numerical results are provided to verify the theoretical analysis.

Broadening of transgenic adenocarcinoma of the mouse prostate (TRAMP) model to represent late stage androgen depletion independent cancer

BACKGROUND The transgenic adenocarcinoma of the mouse prostate (TRAMP) model closely mimics PC-progression as it occurs in humans. However, the timing of disease incidence and progression (especially late stage) makes it logistically difficult to conduct experiments synchronously and economically. The development and characterization of androgen depletion independent (ADI) TRAMP sublines are reported. METHODS Sublines were derived from androgen-sensitive TRAMP-C1 and TRAMP-C2 cell lines by androgen deprivation in vitro and in vivo. Epithelial origin (cytokeratin) and expression of late stage biomarkers (E-cadherin and KAI-1) were evaluated using immunohistochemistry. Androgen receptor (AR) status was assessed through quantitative real time PCR, Western blotting, and immunohistochemistry. Coexpression of AR and E-cadherin was also evaluated. Clonogenicity and invasive potential were measured by soft agar and matrigel invasion assays. Proliferation/survival of sublines in response to androgen was assessed by WST-1 assay. In vivo growth of subcutaneous tumors was assessed in castrated and sham-castrated C57BL/6 mice. RESULTS The sublines were epithelial and displayed ADI in vitro and in vivo. Compared to the parental lines, these showed (1) significantly faster growth rates in vitro and in vivo independent of androgen depletion, (2) greater tumorigenic, and invasive potential in vitro. All showed substantial downregulation in expression levels of tumor suppressor, E-cadherin, and metastatis suppressor, KAI-1. Interestingly, the percentage of cells expressing AR with downregulated E-cadherin was higher in ADI cells, suggesting a possible interaction between the two pathways. CONCLUSIONS The TRAMP model now encompasses ADI sublines potentially representing different phenotypes with increased tumorigenicity and invasiveness.

Mixed convection flow of micropolar fluid in an open ended arc-shape cavity

Numerical simulations for mixed convection of micropolar fluid in an open ended arc-shape cavity have been carried out in this study. Computation is performed using the Alternate Direct Implicit (ADI) method together with the Successive Over Relaxation (SOR) technique for the solution of governing partial differential equations. The flow phenomenon is examined for a range of values of Rayleigh number, 102 ≤ Ra ≤ 106, Prandtl number, 7 ≤ Pr ≤ 50, and Reynolds number, 10 ≤ Re ≤ 100. The study is mainly focused on how the micropolar fluid parameters affect the fluid properties in the flow domain. It was found that despite the reduction of flow in the core region, the heat transfer rate increases, whereas the skin friction and microrotation decrease with the increase in the vortex viscosity parameter, Δ.

Alternating direction implicit numerical method for the space and time fractional Bloch-Torrey equation in 3-D

Recently, some authors have considered a new diffusion model–space and time fractional Bloch-Torrey equation (ST-FBTE). Magin et al. (2008) have derived analytical solutions with fractional order dynamics in space (i.e., _ = 1, β an arbitrary real number, 1 < β ≤ 2) and time (i.e., 0 < α < 1, and β = 2), respectively. Yu et al. (2011) have derived an analytical solution and an effective implicit numerical method for solving ST-FBTEs, and also discussed the stability and convergence of the implicit numerical method. However, due to the computational overheads necessary to perform the simulations for nuclear magnetic resonance (NMR) in three dimensions, they present a study based on a two-dimensional example to confirm their theoretical analysis. Alternating direction implicit (ADI) schemes have been proposed for the numerical simulations of classic differential equations. The ADI schemes will reduce a multidimensional problem to a series of independent one-dimensional problems and are thus computationally efficient. In this paper, we consider the numerical solution of a ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. A fractional alternating direction implicit scheme (FADIS) for the ST-FBTE in 3-D is proposed. Stability and convergence properties of the FADIS are discussed. Finally, some numerical results for ST-FBTE are given.

Targeting aurora kinases : a novel approach to curb the growth and chemoresistance of androgen refractory prostate cancer

Aurora Kinase (AK) based therapy targeting AK-A & B is effective against some cancers. We have explored its potential against previously unreported incurable, metastatic androgen depletion independent Prostate Cancer (ADIPC). We used androgen sensitive (AS) and ADI lines derived from Transgenic Adenocarcinoma of the Mouse Prostate (TRAMP) mice. The relevance of this model was unequivocally established through focussed array, quantitative PCR and western blotting studies; significantly greater alteration of genes (fold change and number) representing major cancer pathways was shown in ADI cells compared to AS lines. A marked enhancement of in vivo growth of the ADI subline showing the greatest degree of gene modulations [TRAMP C1 (TC1)-T5: TC1-T5] reflected this. In contrast to the parental AS TC1 line, TC1-T5 cells grew with 100% incidence in the prostate, as lung pseudometastases and migrated to the bone and other soft tissues. The potential involvement of AKs in this transition was indicated by the significant upregulation of AK-A/B and their downstream regulators, survivin and phosphorylated-histone H3 in TC1-T5 cells compared to TC1 cells. This led to enhanced sensitivity of TC1-T5 cells to the pan-AK inhibitor, VX680 and to significant reduction in in vivo tumour growth rates when AK-A and/or B were downregulated in TC1-T5 cells. This cell growth inhibition was markedly enhanced when both AKs were downregulated and also led to substantially greater sensitivity of these cells to docetaxel, the only chemotherapeutic with activity against ADI PC. Finally, use of VX680 with docetaxel led to impressive synergies suggesting promise for treating clinical ADI metastatic PC.

Gravity-driven fingering simulations for a thin liquid film flowing down the outside of a vertical cylinder

A numerical study is presented to examine the fingering instability of a gravity-driven thin liquid film flowing down the outer wall of a vertical cylinder. The lubrication approximation is employed to derive an evolution equation for the height of the film, which is dependent on a single parameter, the dimensionless cylinder radius. This equation is identified as a special case of that which describes thin film flow down an inclined plane. Fully three-dimensional simulations of the film depict a fingering pattern at the advancing contact line. We find the number of fingers observed in our simulations to be in excellent agreement with experimental observations and a linear stability analysis reported recently by Smolka & SeGall (Phys Fluids 23, 092103 (2011)). As the radius of the cylinder decreases, the modes of perturbation have an increased growth rate, thus increasing cylinder curvature partially acts to encourage the contact line instability. In direct competition with this behaviour, a decrease in cylinder radius means that fewer fingers are able to form around the circumference of the cylinder. Indeed, for a sufficiently small radius, a transition is observed, at which point the contact line is stable to transverse perturbations of all wavenumbers. In this regime, free surface instabilities lead to the development of wave patterns in the axial direction, and the flow features become perfectly analogous to the two-dimensional flow of a thin film down an inverted plane as studied by Lin & Kondic (Phys Fluids 22, 052105 (2010)). Finally, we simulate the flow of a single drop down the outside of the cylinder. Our results show that for drops with low volume, the cylinder curvature has the effect of increasing drop speed and hence promoting the phenomenon of pearling. On the other hand, drops with much larger volume evolve to form single long rivulets with a similar shape to a finger formed in the aforementioned simulations.

Characterization of EhaJ, a new autotransporter protein from enterohemorrhagic and enteropathogenic Escherichia coli

Enterohemorrhagic Escherichia coli (EHEC) and enteropathogenic E. coli (EPEC) are diarrheagenic pathotypes of E. coli that cause gastrointestinal disease with the potential for life-threatening sequelae. While certain EHEC and EPEC virulence mechanisms have been extensively studied, the factors that mediate host colonization remain to be properly defined. Previously, we identified four genes (ehaA, ehaB, ehaC, and ehaD) from the prototypic EHEC strain EDL933 that encode for proteins that belong to the autotransporter (AT) family. Here we have examined the prevalence of these genes, as well as several other AT-encoding genes, in a collection of EHEC and EPEC strains. We show that the complement of AT-encoding genes in EHEC and EPEC strains is variable, with some AT-encoding genes being highly prevalent. One previously uncharacterized AT-encoding gene, which we have termed ehaJ, was identified in 12/44 (27%) of EHEC and 2/20 (10%) of EPEC strains. The ehaJ gene lies immediately adjacent to a gene encoding a putative glycosyltransferase (referred to as egtA). Western blot analysis using an EhaJ-specific antibody indicated that EhaJ is glycosylated by EgtA. Expression of EhaJ in a recombinant E. coli strain, revealed EhaJ is located at the cell surface and in the presence of the egtA glycosyltransferase gene mediates strong biofilm formation in microtiter plate and flow cell assays. EhaJ also mediated adherence to a range of extracellular matrix proteins, however this occurred independent of glycosylation. We also demonstrate that EhaJ is expressed in a wild-type EPEC strain following in vitro growth. However, deletion of ehaJ did not significantly alter its adherence or biofilm properties. In summary, EhaJ is a new glycosylated AT protein from EPEC and EHEC. Further studies are required to elucidate the function of EhaJ in colonization and virulence.

Escherichia coli 83972 expressing a P fimbriae oligosaccharide receptor mimic impairs adhesion of Uropathogenic E. coli

Urinary tract infections (UTIs) caused by uropathogenic Escherichia coli (UPEC) are a significant health concern, exacerbated by the rapid emergence of multidrug resistant strains refractory to antibiotic treatment. P fimbriae are strongly associated with upper urinary tract colonization due to specific binding to α-D-galactopyranosyl-(1-4)-β-D-galactopyranoside receptors in the kidneys. Thus, inhibiting P-fimbrial adhesion may reduce the incidence of UPEC-mediated UTI. E. coli 83972 is an asymptomatic bacteriuria isolate successfully used as a prophylactic agent to prevent UTI in human studies. We constructed a recombinant E. coli 83972 strain displaying a surface-located oligosaccharide P fimbriae receptor mimic that bound to P-fimbriated E. coli producing any of the 3 PapG adhesin variants. The recombinant strain, E. coli 83972:: lgtCE, impaired P fimbriae–mediated adhesion to human erythrocytes and kidney epithelial cells. Additionally, E. coli 83972::lgtCE impaired urine colonization by UPEC in a mouse UTI model, demonstrating its potential as a prophylactic agent to prevent UTI.

Uropathogenic Escherichia coli mediated urinary tract infection

Urinary tract infection (UTI) is among the most common infectious diseases of humans and is the most common nosocomial infection in the developed world. They cause significant morbidity and mortality, with approximately 150 million cases globally per year. It is estimated that 40-50% of women and 5% of men will develop a UTI in their lifetime, and UTI accounts for more than 1 million hospitalizations and $1.6 billion in medical expenses each year in the USA. Uropathogenic E. coli (UPEC) is the primary cause of UTI. This review presents an overview of the primary virulence factors of UPEC, the major host responses to infection of the urinary tract, the emergence of specific multidrug resistant clones of UPEC, antibiotic treatment options for UPEC-mediated UTI and the current state of vaccine strategies as well as other novel anti-adhesive and prophylactic approaches to prevent UTI. New and emerging themes in UPEC research are also discussed in the context of future outlooks.

Double diffusive Marangoni convection flow of electrically conducting fluid in a square cavity with chemical reaction

Double diffusive Marangoni convection flow of viscous incompressible electrically conducting fluid in a square cavity is studied in this paper by taking into consideration of the effect of applied magnetic field in arbitrary direction and the chemical reaction. The governing equations are solved numerically by using alternate direct implicit (ADI) method together with the successive over relaxation (SOR) technique. The flow pattern with the effect of governing parameters, namely the buoyancy ratio W, diffusocapillary ratio w, and the Hartmann number Ha, is investigated. It is revealed from the numerical simulations that the average Nusselt number decreases; whereas the average Sherwood number increases as the orientation of magnetic field is shifted from horizontal to vertical. Moreover, the effect of buoyancy due to species concentration on the flow is stronger than the one due to thermal buoyancy. The increase in diffusocapillary parameter, w caus

A computer code for enclosed natural convection in the boundary layer regime

A computer code is developed for the numerical prediction of natural convection in rectangular two-dimensional cavities at high Rayleigh numbers. The governing equations are retained in the primitive variable form. The numerical method is based on finite differences and an ADI scheme. Convective terms may be approximated with either central or hybrid differencing for greater stability. A non-uniform grid distribution is possible for greater efficiency. The pressure is dealt with via a SIMPLE type algorithm and the use of a fast elliptic solver for the solenoidal velocity correction field significantly reduces computing times. Preliminary results indicate that the code is reasonably accurate, robust and fast compared with existing benchmarks and finite difference based codes, particularly at high Rayleigh numbers. Extension to three-dimensional problems and turbulence studies in similar geometries is readily possible and indicated.