Eigenvalues of higher order Sturm-Liouville boundary value problems with derivatives in nonlinear terms

We shall consider the Sturm-Liouville boundary value problem y(m)(t)+λF(t,y(t),y′(t),…,y(q)(t))=0, t∈(0,1), y(k)(0)=0, 0≤k≤m−3, ζy(m−2)(0)−θy(m−1)(0)=0, ρy(m−2)(1)+δy(m−1)(1)=0 where m≥3, 1≤q≤m−2, and λ>0. It is noted that the boundary value problem considered has a derivative-dependent nonlinear term, which makes the investigation much more challenging. In this paper we shall develop a new technique to characterize the eigenvalues λ so that the boundary value problem has a positive solution. Explicit eigenvalue intervals are also established. Some examples are included to dwell upon the usefulness of the results obtained.Published versio

Functional Analysis of Host Factors that Mediate the Intracellular Lifestyle of Cryptococcus neoformans

Cryptococcus neoformans (Cn), the major causative agent of human fungal meningoencephalitis, replicates within phagolysosomes of infected host cells. Despite more than a half-century of investigation into host-Cn interactions, host factors that mediate infection by this fungal pathogen remain obscure. Here, we describe the development of a system that employs Drosophila S2 cells and RNA interference (RNAi) to define and characterize Cn host factors. The system recapitulated salient aspects of fungal interactions with mammalian cells, including phagocytosis, intracellular trafficking, replication, cell-to-cell spread and escape of the pathogen from host cells. Fifty-seven evolutionarily conserved host factors were identified using this system, including 29 factors that had not been previously implicated in mediating fungal pathogenesis. Subsequent analysis indicated that Cn exploits host actin cytoskeletal elements, cell surface signaling molecules, and vesicle-mediated transport proteins to establish a replicative niche. Several host molecules known to be associated with autophagy (Atg), including Atg2, Atg5, Atg9 and Pi3K59F (a class III PI3-kinase) were also uncovered in our screen. Small interfering RNA (siRNA) mediated depletion of these autophagy proteins in murine RAW264.7 macrophages demonstrated their requirement during Cn infection, thereby validating findings obtained using the Drosophila S2 cell system. Immunofluorescence confocal microscopy analyses demonstrated that Atg5, LC3, Atg9a were recruited to the vicinity of Cn containing vacuoles (CnCvs) in the early stages of Cn infection. Pharmacological inhibition of autophagy and/or PI3-kinase activity further demonstrated a requirement for autophagy associated host proteins in supporting infection of mammalian cells by Cn. Finally, systematic trafficking studies indicated that CnCVs associated with Atg proteins, including Atg5, Atg9a and LC3, during trafficking to a terminal intracellular compartment that was decorated with the lysosomal markers LAMP-1 and cathepsin D. Our findings validate the utility of the Drosophila S2 cell system as a functional genomic platform for identifying and characterizing host factors that mediate fungal intracellular replication. Our results also support a model in which host Atg proteins mediate Cn intracellular trafficking and replication

Effect of sitagliptin on cardiovascular outcomes in type 2 diabetes

BACKGROUND: Data are lacking on the long-term effect on cardiovascular events of adding sitagliptin, a dipeptidyl peptidase 4 inhibitor, to usual care in patients with type 2 diabetes and cardiovascular disease. METHODS: In this randomized, double-blind study, we assigned 14,671 patients to add either sitagliptin or placebo to their existing therapy. Open-label use of antihyperglycemic therapy was encouraged as required, aimed at reaching individually appropriate glycemic targets in all patients. To determine whether sitagliptin was noninferior to placebo, we used a relative risk of 1.3 as the marginal upper boundary. The primary cardiovascular outcome was a composite of cardiovascular death, nonfatal myocardial infarction, nonfatal stroke, or hospitalization for unstable angina. RESULTS: During a median follow-up of 3.0 years, there was a small difference in glycated hemoglobin levels (least-squares mean difference for sitagliptin vs. placebo, -0.29 percentage points; 95% confidence interval [CI], -0.32 to -0.27). Overall, the primary outcome occurred in 839 patients in the sitagliptin group (11.4%; 4.06 per 100 person-years) and 851 patients in the placebo group (11.6%; 4.17 per 100 person-years). Sitagliptin was noninferior to placebo for the primary composite cardiovascular outcome (hazard ratio, 0.98; 95% CI, 0.88 to 1.09; P<0.001). Rates of hospitalization for heart failure did not differ between the two groups (hazard ratio, 1.00; 95% CI, 0.83 to 1.20; P = 0.98). There were no significant between-group differences in rates of acute pancreatitis (P = 0.07) or pancreatic cancer (P = 0.32). CONCLUSIONS: Among patients with type 2 diabetes and established cardiovascular disease, adding sitagliptin to usual care did not appear to increase the risk of major adverse cardiovascular events, hospitalization for heart failure, or other adverse events

Xyloketal-derived small molecules show protective effect by decreasing mutant Huntingtin protein aggregates in Caenorhabditis elegans model of Huntington&rsquo;s disease

Yixuan Zeng,1,2,* Wenyuan Guo,1,* Guangqing Xu,3 Qinmei Wang,4 Luyang Feng,1,2 Simei Long,1 Fengyin Liang,1 Yi Huang,1 Xilin Lu,1 Shichang Li,5 Jiebin Zhou,5 Jean-Marc Burgunder,6 Jiyan Pang,5 Zhong Pei1,2 1Department of Neurology, National Key Clinical Department and Key Discipline of Neurology, Guangdong Key Laboratory for Diagnosis and Treatment of Major Neurological Disease, The First Affiliated Hospital, Sun Yat-sen University, 2Guangzhou Center, Chinese Huntington&rsquo;s Disease Network, 3Department of Rehabilitation, The First Affiliated Hospital, 4Key laboratory on Assisted Circulation, Ministry of Health, Department of Cardiovascular Medicine of the First Affiliated Hospital, 5School of Chemistry and Chemical Engineering, Sun Yat-sen University, Guangzhou, Guangdong, People&rsquo;s Republic of China; 6Swiss Huntington&rsquo;s Disease Center, Department of Neurology, University of Bern, Bern, Switzerland *These authors contributed equally to this work Abstract: Huntington&rsquo;s disease is an autosomal-dominant neurodegenerative disorder, with chorea as the most prominent manifestation. The disease is caused by abnormal expansion of CAG codon repeats in the IT15 gene, which leads to the expression of a glutamine-rich protein named mutant Huntingtin (Htt). Because of its devastating disease burden and lack of valid treatment, development of more effective therapeutics for Huntington&rsquo;s disease is urgently required. Xyloketal B, a natural product from mangrove fungus, has shown protective effects against toxicity in other neurodegenerative disease models such as Parkinson&rsquo;s and Alzheimer&rsquo;s diseases. To identify potential neuroprotective molecules for Huntington&rsquo;s disease, six derivatives of xyloketal B were screened in a Caenorhabditis elegans Huntington&rsquo;s disease model; all six compounds showed a protective effect. Molecular docking studies indicated that compound&nbsp;1 could bind to residues GLN369 and GLN393 of the mutant Htt protein, forming a stable trimeric complex that can prevent the formation of mutant Htt aggregates. Taken together, we conclude that xyloketal derivatives could be novel drug candidates for treating Huntington&rsquo;s disease. Molecular target analysis is a good method to simulate the interaction between proteins and drug compounds. Further, protective candidate drugs could be designed in future using the guidance of molecular docking results. Keywords: Huntington&rsquo;s disease, mutant Huntingtin, xyloketal derivatives, Caenorhabditis elegans, protein misfolding, molecular targe