Singular solutions of fully nonlinear elliptic equations and applications

We study the properties of solutions of fully nonlinear, positively homogeneous elliptic equations near boundary points of Lipschitz domains at which the solution may be singular. We show that these equations have two positive solutions in each cone of $\mathbb{R}^n$, and the solutions are unique in an appropriate sense. We introduce a new method for analyzing the behavior of solutions near certain Lipschitz boundary points, which permits us to classify isolated boundary singularities of solutions which are bounded from either above or below. We also obtain a sharp Phragm\'en-Lindel\"of result as well as a principle of positive singularities in certain Lipschitz domains.Comment: 41 pages, 2 figure

How to develop and prove high-efficiency selection of ligands from oligonucleotide libraries: A universal framework for aptamers and DNA-Encoded small-molecule ligands

Screening molecular libraries for ligands capable of binding proteins is widely used for hit identification in the early drug discovery process. Oligonucleotide libraries provide a very high diversity of compounds, while the combination of the polymerase chain reaction and DNA sequencing allow the identification of ligands in low copy numbers selected from such libraries. Ligand selection from oligonucleotide libraries requires mixing the library with the target followed by the physical separation of the ligand–target complexes from the unbound library. Cumulatively, the low abundance of ligands in the library and the low efficiency of available separation methods necessitate multiple consecutive rounds of partitioning. Multiple rounds of inefficient partitioning make the selection process ineffective and prone to failures. There are continuing efforts to develop a separation method capable of reliably generating a pure pool of ligands in a single round of partitioning; however, none of the proposed methods for single-round selection have been universally adopted. Our analysis revealed that the developers’ efforts are disconnected from each other and hindered by the lack of quantitative criteria of selection quality assessment. Here, we present a formalism that describes single-round selection mathematically and provides parameters for quantitative characterization of selection quality. We use this formalism to define a universal strategy for development and validation of single-round selection methods. Finally, we analyze the existing partitioning methods, the published single-round selection reports, and some pertinent practical considerations through the prism of this formalism. This formalism is not an experimental protocol but a framework for correct development of experimental protocols. While single-round selection is not a goal by itself and may not always suffice selection of good-quality ligands, our work will help developers of highly efficient selection approaches to consolidate their efforts under an umbrella of universal quantitative criteria of method development and assessment

Low expression of miR-126 Is a prognostic marker for metastatic clear cell renal cell carcinoma

Clear cell renal cell carcinoma (ccRCC) is an aggressive tumor with unpredictable behavior. Clinical parameters are not always accurate for predicting prognosis. miR-126 is differentially expressed in many cancers, including RCC, and is down-regulated in metastatic versus primary ccRCC. We assessed the prognostic significance of miR-126 in 264 primary ccRCCs. We also compared its expression in normal kidney, primary and metastatic ccRCC, and RCC subtypes. We validated our results on an independent set of 481 ccRCCs. miR-126 was down-regulated in metastatic versus primary tumors and in tumors of higher stage (P = 0.005) or higher grade (P = 0.002). miR-126 up-regulation was associated with significantly prolonged disease-free survival (P < 0.001) and overall survival (P = 0.015). For larger tumors (>4 cm), patients with higher miR-126 expression had significantly longer survival. Restoration of miR-126 expression decreased cellular migration and proliferation in RCC cell lines. The ccRCCs exhibited the highest miR-126 expression, and papillary RCCs exhibited the lowest expression. We identified a number of miR-126 targets and pathways that are involved in carcinogenesis, including the apoptosis signaling pathway. miR-126 is a promising prognostic marker in ccRCC that can distinguish between clear cell and papillary subtypes. In addition, miR-126 has potential therapeutic applications. © 2015 American Society for Investigative Pathology

MiR-210 is a prognostic marker in clear cell renal cell carcinoma

Accurate assessment of prognosis of clear cell renal cell carcinoma (ccRCC) is key in optimizing management plans to fit individual patient needs. miRNAs are short noncoding single-stranded RNAs that control the expression of target genes and may act as cancer biomarkers. We analyzed the expression of miR-210 in 276 cases of primary ccRCC and compared its expression in 40 pairs of adjacent normal and cancerous tissues. We assessed its expression in primary and metastatic tumors, in the common RCC subtypes, and the benign oncocytoma. The results were validated with an independent data set from The Cancer Genome Atlas. miR-210 was significantly overexpressed in ccRCC compared with normal kidney. miR-210+ patients had a statistically higher chance of disease recurrence [hazard ratio (HR), 1.82; P = 0.018] and shorter overall survival (HR, 2.46; P = 0.014). In multivariate analysis, miR-210 lost its statistically significant association with shorter disease-free survival and overall survival after adjusting for tumor size and tumor, node, metastasis stage. Papillary RCC showed comparable miR-210 overexpression, whereas decreased up-regulation was seen in chromophobe RCC and oncocytoma. A number of predicted targets that might be involved in carcinogenesis and aggressive tumor behavior were identified. miR-210 is a potential therapeutic target and independent marker of poor prognosis of ccRCC. © 2015 American Society for Investigative Pathology and the Association for Molecular Pathology