A Second-Order Boundary Value Problem with Nonlinear and Mixed Boundary Conditions: Existence, Uniqueness, and Approximation

A second-order boundary value problem with nonlinear and mixed two-point boundary conditions is considered, Lx=f(t,x,x′), t∈(a,b), g(x(a),x(b),x′(a),x′(b))=0, x(b)=x(a) in which L is a formally self-adjoint second-order differential operator. Under appropriate assumptions on L, f, and g, existence and uniqueness of solutions is established by the method of upper and lower solutions and Leray-Schauder degree theory. The general quasilinearization method is then applied to this problem. Two monotone sequences converging quadratically to the unique solution are constructed

Optimising the Use of TRIzol-extracted Proteins in Surface Enhanced Laser Desorption/ Ionization (SELDI) Analysis

BACKGROUND: Research with clinical specimens is always hampered by the limited availability of relevant samples, necessitating the use of a single sample for multiple assays. TRIzol is a common reagent for RNA extraction, but DNA and protein fractions can also be used for other studies. However, little is known about using TRIzol-extracted proteins in proteomic research, partly because proteins extracted from TRIzol are very resistant to solubilization. RESULTS: To facilitate the use of TRIzol-extracted proteins, we first compared the ability of four different common solubilizing reagents to solubilize the TRIzol-extracted proteins from an osteosarcoma cell line, U2-OS. Then we analyzed the solubilized proteins by Surface Enhanced Laser Desorption/ Ionization technique (SELDI). The results showed that solubilization of TRIzol-extracted proteins with 9.5 M Urea and 2% CHAPS ([3-[(3-cholamidopropyl)-dimethylammonio]propanesulfonate]) (UREA-CHAPS) was significantly better than the standard 1% SDS in terms of solubilization efficiency and the number of detectable ion peaks. Using three different types of SELDI arrays (CM10, H50, and IMAC-Cu), we demonstrated that peak detection with proteins solubilized by UREA-CHAPS was reproducible (r > 0.9). Further SELDI analysis indicated that the number of ion peaks detected in TRIzol-extracted proteins was comparable to a direct extraction method, suggesting many proteins still remain in the TRIzol protein fraction. CONCLUSION: Our results suggest that UREA-CHAPS performed very well in solubilizing TRIzol-extracted proteins for SELDI applications. Protein fractions left over after TRIzol RNA extraction could be a valuable but neglected source for proteomic or biochemical analysis when additional samples are not available

Integrated DNA Copy Number and Expression Profiling Identifies IGF1R as a Prognostic Biomarker in Pediatric Osteosarcoma.

Osteosarcoma is a primary malignant bone tumor arising from bone-forming mesenchymal cells in children and adolescents. Despite efforts to understand the biology of the disease and identify novel therapeutics, the survival of osteosarcoma patients remains dismal. We have concurrently profiled the copy number and gene expression of 226 osteosarcoma samples as part of the Strategic Partnering to Evaluate Cancer Signatures (SPECS) initiative. Our results demonstrate the heterogeneous landscape of osteosarcoma in younger populations by showing the presence of genome-wide copy number abnormalities occurring both recurrently among samples and in a high frequency. Insulin growth factor receptor 1 (IGF1R) is a receptor tyrosine kinase which binds IGF1 and IGF2 to activate downstream pathways involved in cell apoptosis and proliferation. We identify prevalent amplification of IGF1R corresponding with increased gene expression in patients with poor survival outcomes. Our results substantiate previously tenuously associated copy number abnormalities identified in smaller datasets (13q34+, 20p13+, 4q35-, 20q13.33-), and indicate the significance of high fibroblast growth factor receptor 2 (FGFR2) expression in distinguishing patients with poor prognosis. FGFR2 is involved in cellular proliferation processes such as division, growth and angiogenesis. In summary, our findings demonstrate the prognostic significance of several genes associated with osteosarcoma pathogenesis

Maximizing the potential of aggressive mouse tumor models in preclinical drug testing.

Atypical teratoid rhabdoid tumor (ATRT) is an aggressive embryonal brain tumor among infants and young children. Two challenges exist for preclinical testing in ATRT. First, genetically quiet, ATRT is a difficult tumor to target molecularly. Tumor cells need to divide to propagate tumor growth-intercepting the common crossroads in cell cycle progression is a feasible strategy. KIF11 is needed for bipolar spindle formation in metaphase. We identified KIF11 as a universal target of all ATRT-molecular-subtypes. Ispinesib, a KIF11-inhibitor, effectively inhibited tumor proliferation in all seven cell lines. A second challenge-a major challenge in preclinical drug testing in-vivo among aggressive tumor models, is the narrow therapeutic window to administer drugs within the limited murine lifespan. Our most aggressive ATRT tumor model was lethal in all mice within ~ 1 month of tumor implantation. Such short-surviving mouse models are difficult to employ for preclinical drug testing due to the narrow time window to administer drugs. To overcome this time restriction, we developed a clinical staging system which allowed physically-fit mice to continue treatment, in contrast to the conventional method of fixed drug-dose-duration regimen in preclinical testing which will not be feasible in such short-surviving mouse models. We validated this approach in a second embryonal brain tumor, medulloblastoma. This is a clinically relevant, cost-efficient approach in preclinical testing for cancer and non-cancer disease phenotypes. Widely used preclinical mouse models are not the most accurate and lack the aggressive tumor spectrum found within a single tumor type. Mice bearing the most aggressive tumor spectrum progress rapidly in the limited murine life-span, resulting in a narrow therapeutic window to administer drugs, and are thus difficult to employ in preclinical testing. Our approach overcomes this challenge. We discovered ispinesib is efficacious against two embryonal brain tumor types

Fast–Slow Dynamics for Intraguild Predation Models with Evolutionary Effects

[[abstract]]This work is concerned with the fast–slow dynamics for intraguild predation models with evolutionary effects. Assuming the survival pressure of the weaker predator induces evolution of it to the intraguild predator, then the system can be viewed as a singularly perturbed problem with two different time scales—predation time scale and evolution time scale. Using the geometric singular perturbation theory, we first completely analyze the limiting slow–fast dynamics of the system which involve the existence of turning points. Then, an application of the geometric singular perturbation theory gives rise to the birth of relaxation oscillations caused by the turning points and the associated delay of stability loss. From our main results, one can see that evolution enhances survival rates of inferior competitors.[[notice]]補正完

Pulse dynamics in reaction-diffusion equations with strong spatially localized impurities

In this article, a general geometric singular perturbation framework is developed to study the impact of strong, spatially localized, nonlinear impurities on the existence, stability and bifurcations of localized structures in systems of linear reaction–diffusion equations. By taking advantage of the multiple-scale nature of the problem, we derive algebraic conditions determining the existence and stability of pinned single- and multi-pulse solutions. Our methods enable us to explicitly control the spectrum associated with a (multi-)pulse solution. In the scalar case, we show how eigenvalues may move in and out of the essential spectrum and that Hopf bifurcations cannot occur. By contrast, even a pinned 1-pulse solution can undergo a Hopf bifurcation in a two-component system of linear reaction–diffusion equations with (only) one impurity. This article is part of the theme issue ‘Stability of nonlinear waves and patterns and related topics’

Relaxation Oscillations in Singularly Perturbed Generalized Lienard Systems with Non-Generic Turning Points

Based on the asymptotic analysis technique developed by Eckhaus [Lecture Notes in Math., vol. 985, pp 449-494. Springer, Berlin, 1983], this paper aims to study the existence and the asymptotic behaviors of relaxation oscillations of regular and canard types in a singularly perturbed generalized Lionard system with a non-generic turning point. The singularly perturbed Lionard system considered in this paper is very general and numerous real world models like some biological ones can be rewritten in the form of this system after a series of transformations. Under certain conditions, we rigorously prove the existence of regular relaxation oscillations and canard relaxation oscillations under the specific parameter conditions. As an application, two biological models, namely, a FitzHugh-Nagumo model and a twodimensional predator-prey model with Holling-II response are studied, in which, the existence of regular relaxation oscillations and canard relaxation oscillations as well as the bifurcation curves are obtained

Recombinant Antimicrobial Peptide OaBac5mini Alleviates Inflammation in Pullorum Disease Chicks by Modulating TLR4/MyD88/NF-κB Pathway

Pullorum disease (PD), caused by Salmonella Pullorum (S. Pullorum), is a serious threat to the poultry industry worldwide. Antimicrobial peptides (AMPs) have drawn extensive attention as new-generation antibiotics because of their broad antimicrobial spectrum, low resistance, and low cytotoxicity. AMP OaBac5mini exhibits strong antibacterial activity against Gram-negative bacteria, but its efficacy and anti-inflammatory effects on chicks with PD remain unclear. The aim of this study was to generate recombinant OaBac5mini via the Escherichia coli (E. coli) recombinant expression system and evaluate its antibacterial effect against S. Pullorum in vitro and in vivo. Real-time cellular analysis (RTCA) results showed that recombinant OaBac5mini exhibited no cytotoxicity on IPEC-J2 and RAW 264.7 cells and significantly alleviated the drop in the cell index of S. Pullorum-infected cells (p S. Pullorum. Histopathology examination showed that recombinant OaBac5mini ameliorated histopathological changes and inflammation in chicks with PD, including impaired epithelium of duodenal villi, infiltration of pseudoacidophilic granulocytes in the cecum and bursa of Fabricius, congested blood clots and increased macrophages in the liver, and increased lymphoid nodule and B lymphocytes in the spleen. Western blot and quantitative real-time PCR (qRT-PCR) results indicated that recombinant OaBac5mini alleviated inflammation by modulating innate immunity through the TLR4/MyD88/NF-κB pathway and by suppressing the expression of pro-inflammatory cytokines. These results suggested that recombinant OaBac5mini has good potential as a clinical substitute for antibiotics in PD intervention