Isolated singularities of polyharmonic operator in even dimension

We consider the equation Delta(2)u = g(x, u) >= 0 in the sense of distribution in Omega' = Omega\textbackslash {0} where u and -Delta u >= 0. Then it is known that u solves Delta(2)u = g(x, u) + alpha delta(0) - beta Delta delta(0), for some nonnegative constants alpha and beta. In this paper, we study the existence of singular solutions to Delta(2)u = a(x) f (u) + alpha delta(0) - beta Delta delta(0) in a domain Omega subset of R-4, a is a nonnegative measurable function in some Lebesgue space. If Delta(2)u = a(x) f (u) in Omega', then we find the growth of the nonlinearity f that determines alpha and beta to be 0. In case when alpha = beta = 0, we will establish regularity results when f (t) <= Ce-gamma t, for some C, gamma > 0. This paper extends the work of Soranzo (1997) where the author finds the barrier function in higher dimensions (N >= 5) with a specific weight function a(x) = |x|(sigma). Later, we discuss its analogous generalization for the polyharmonic operator.

Genomic amplification upregulates estrogen-related receptor alpha and its depletion inhibits oral squamous cell carcinoma tumors in vivo

The ESRRA gene encodes a transcription factor and regulates several genes, such as WNT11 and OPN, involved in tumorigenesis. It is upregulated in several cancers, including OSCC. We have previously shown that the tumor suppressor miR-125a targets ESRRA, and its downregulation causes upregulation of ESRRA in OSCC. Upregulation of ESRRA in the absence of downregulation of miR-125a in a subset of OSCC samples suggests the involvement of an alternative mechanism. Using TaqMan (R) copy number assay, here we report for the first time that the genomic amplification of ESRRA causes its upregulation in a subset of OSCC samples. Ectopic overexpression of ESRRA led to accelerated cell proliferation, anchorage-independent cell growth and invasion, and inhibited apoptosis. Whereas, knockdown of ESRRA expression by siRNA led to reduced cell proliferation, anchorage-independent cell growth and invasion, and accelerated apoptosis. Furthermore, the delivery of a synthetic biostable ESRRA siRNA to OSCC cells resulted in regression of xenografts in nude mice. Thus, the genomic amplification of ESRRA is another novel mechanism for its upregulation in OSCC. Based on our in vitro and in vivo experiments, we suggest that targeting ESRRA by siRNA could be a novel therapeutic strategy for OSCC and other cancers.

Polyketide Quinones Are Alternate Intermediate Electron Carriers during Mycobacterial Respiration in Oxygen-Deficient Niches

Mycobacterium tuberculosis (Mtb) adaptation to hypoxia is considered crucial to its prolonged latent persistence in humans. Mtb lesions are known to contain physiologically heterogeneous microenvironments that bring about differential responses from bacteria. Here we exploit metabolic variability within biofilm cells to identify alternate respiratory polyketide quinones (PkQs) from both Mycobacterium smegmatis (Msmeg) and Mtb. PkQs are specifically expressed in biofilms and other oxygen-deficient niches to maintain cellular bioenergetics. Under such conditions, these metabolites function as mobile electron carriers in the respiratory electron transport chain. In the absence of PkQs, mycobacteria escape from the hypoxic core of biofilms and prefer oxygenrich conditions. Unlike the ubiquitous isoprenoid pathway for the biosynthesis of respiratory quinones, PkQs are produced by type III polyketide synthases using fatty acyl-CoA precursors. The biosynthetic pathway is conserved in several other bacterial genomes, and our study reveals a redox-balancing chemicocellular process in microbial physiology.