Uniqueness of the potential function for the vectorial Sturm-Liouville equation on a finite interval

[[abstract]]In this paper, the vectorial Sturm-Liouville operator L Q =−d 2 dx 2 +Q(x) is considered, where Q(x) is an integrable m×m matrix-valued function defined on the interval [0,π] . The authors prove that m 2 +1 characteristic functions can determine the potential function of a vectorial Sturm-Liouville operator uniquely. In particular, if Q(x) is real symmetric, then m(m+1) 2 +1 characteristic functions can determine the potential function uniquely. Moreover, if only the spectral data of self-adjoint problems are considered, then m 2 +1 spectral data can determine Q(x) uniquely.[[notice]]補正完畢[[incitationindex]]SCI[[cooperationtype]]國外[[booktype]]電子

Matrix Metalloproteinase-10 Is Required for Lung Cancer Stem Cell Maintenance, Tumor Initiation and Metastatic Potential

Matrix metalloproteinases (Mmps) stimulate tumor invasion and metastasis by degrading the extracellular matrix. Here we reveal an unexpected role for Mmp10 (stromelysin 2) in the maintenance and tumorigenicity of mouse lung cancer stem-like cells (CSC). Mmp10 is highly expressed in oncosphere cultures enriched in CSCs and RNAi-mediated knockdown of Mmp10 leads to a loss of stem cell marker gene expression and inhibition of oncosphere growth, clonal expansion, and transformed growth in vitro. Interestingly, clonal expansion of Mmp10 deficient oncospheres can be restored by addition of exogenous Mmp10 protein to the culture medium, demonstrating a direct role for Mmp10 in the proliferation of these cells. Oncospheres exhibit enhanced tumor-initiating and metastatic activity when injected orthotopically into syngeneic mice, whereas Mmp10-deficient cultures show a severe defect in tumor initiation. Conversely, oncospheres implanted into syngeneic non-transgenic or Mmp10−/− mice show no significant difference in tumor initiation, growth or metastasis, demonstrating the importance of Mmp10 produced by cancer cells rather than the tumor microenvironment in lung tumor initiation and maintenance. Analysis of gene expression data from human cancers reveals a strong positive correlation between tumor Mmp10 expression and metastatic behavior in many human tumor types. Thus, Mmp10 is required for maintenance of a highly tumorigenic, cancer-initiating, metastatic stem-like cell population in lung cancer. Our data demonstrate for the first time that Mmp10 is a critical lung cancer stem cell gene and novel therapeutic target for lung cancer stem cells

Pre-microRNA and Mature microRNA in Human Mitochondria

Chantier qualité GAInternational audienceBACKGROUND: Because of the central functions of the mitochondria in providing metabolic energy and initiating apoptosis on one hand and the role that microRNA (miRNA) play in gene expression, we hypothesized that some miRNA could be present in the mitochondria for post-transcriptomic regulation by RNA interference. We intend to identify miRNA localized in the mitochondria isolated from human skeletal primary muscular cells. METHODOLOGY/PRINCIPAL FINDINGS: To investigate the potential origin of mitochondrial miRNA, we in-silico searched for microRNA candidates in the mtDNA. Twenty five human pre-miRNA and 33 miRNA aligments (E-value35) for the smallest RNA input concentration and 204 miRNA for the maximum RNA input concentration. In silico analysis predicted 80 putative miRNA target sites in the mitochondrial genome (E-value<0.05). CONCLUSIONS/SIGNIFICANCE: The present study experimentally demonstrated for the first time the presence of pre-miRNA and miRNA in the human mitochondria isolated from skeletal muscular cells. A set of miRNA were significantly detected in mitochondria fraction. The origin of these pre-miRNA and miRNA should be further investigate to determine if they are imported from the cytosol and/or if they are partially processed in the mitochondria

Nuclear Outsourcing of RNA Interference Components to Human Mitochondria

MicroRNAs (miRNAs) are small non-coding RNAs that associate with Argonaute proteins to regulate gene expression at the post-transcriptional level in the cytoplasm. However, recent studies have reported that some miRNAs localize to and function in other cellular compartments. Mitochondria harbour their own genetic system that may be a potential site for miRNA mediated post-transcriptional regulation. We aimed at investigating whether nuclear-encoded miRNAs can localize to and function in human mitochondria. To enable identification of mitochondrial-enriched miRNAs, we profiled the mitochondrial and cytosolic RNA fractions from the same HeLa cells by miRNA microarray analysis. Mitochondria were purified using a combination of cell fractionation and immunoisolation, and assessed for the lack of protein and RNA contaminants. We found 57 miRNAs differentially expressed in HeLa mitochondria and cytosol. Of these 57, a signature of 13 nuclear-encoded miRNAs was reproducibly enriched in mitochondrial RNA and validated by RT-PCR for hsa-miR-494, hsa-miR-1275 and hsa-miR-1974. The significance of their mitochondrial localization was investigated by characterizing their genomic context, cross-species conservation and instrinsic features such as their size and thermodynamic parameters. Interestingly, the specificities of mitochondrial versus cytosolic miRNAs were underlined by significantly different structural and thermodynamic parameters. Computational targeting analysis of most mitochondrial miRNAs revealed not only nuclear but also mitochondrial-encoded targets. The functional relevance of miRNAs in mitochondria was supported by the finding of Argonaute 2 localization to mitochondria revealed by immunoblotting and confocal microscopy, and further validated by the co-immunoprecipitation of the mitochondrial transcript COX3. This study provides the first comprehensive view of the localization of RNA interference components to the mitochondria. Our data outline the molecular bases for a novel layer of crosstalk between nucleus and mitochondria through a specific subset of human miRNAs that we termed ‘mitomiRs’

Minimal realizations of scalar generalized Nevanlinna functions related to their basic factorization

In this paper we present a minimal realization of a scalar generalized Nevanlinna function q which corresponds to the basic factorization of q as a product of a Nevanlinna function q(0) and of a rational function r(#)r, which collects the generalized poles and generalized zeros of q that are not of positive type. The key tool are reproducing kernel Pontryagin spaces.</p