A class of second order BVPs on infinite intervals

In this work, we are concerned with a boundary value problem associated with a generalized Fisher-like equation. This equation involves an eigenvalue and a parameter which may be viewed as a wave speed. According to the behavior of the nonlinear source term, existence results of bounded solutions, positive solutions, classical as well as weak solutions are provided. We mainly use fixed point arguments

Systems of φ-Laplacian three-point boundary-value problems on the positive half-line

We study the existence of positive solutions to boundary-value problems for two systems of two second-order nonlinear three-point φ-Laplacian equations defined on the positive half line. The nonlinearities may change sign, exhibit time singularities at the origin, and depend both on the solutions and on their first derivatives. Using the fixed-point theory, we prove some results on the existence of nontrivial positive solutions on appropriate cones in some weighted Banach spaces.Вивчається iснування додатних розв’язкiв граничних задач для двох систем двох нелiнiйних триточкових φ-лапласових рiвнянь другого порядку, що визначенi на додатнiй пiвосi. Нелiнiйностi можуть змiнювати знак, мати часовi сингулярностi на початку координат та залежати, як вiд розв’язкiв, так i вiд їх перших похiдних. Теорiю нерухомих точок застосовано для доведення деяких результатiв щодо iснування нетривiальних додатнiх розв’язкiв на вiдповiдних конусах в деяких звaжених банахових просторах

Positive solutions for singular ϕ−\phi-Laplacian BVPs on the positive half-line

In this work, we are concerned with the existence of positive solutions for a $\phi$ Laplacian boundary value problem on the half-line. The results are proved using the fixed point index theory on cones of Banach spaces and the upper and lower solution technique. The nonlinearity may exhibit a singularity at the origin with respect to the solution. This singularity is treated by regularization and approximation together with compactness and sequential arguments

System of singular second-order differential equations with integral condition on the positive half-line

In this work, we are concerned with the existence and the multiplicity of nontrivial positive solutions for a boundary value problem of a system of second-order differential equations subject to an integral boundary condition and posed on the positive half-line. The positive nonlinearities depend on the solution and their derivatives and may have space singularities. New existence results of single and multiple solutions are obtained by means of the fixed point index theory on special cones in some weighted Banach space. Examples with numerical computations are included to illustrate the obtained existence theorems. This paper surveys and generalizes previous works

Boundary value problems for doubly perturbed first order ordinary differential systems

The aim of this paper is to present new results on existence theory for perturbed BVPs for first order ordinary differential systems. A nonlinear alternative for the sum of a contraction and a compact mapping is used

The Degasperis-Procesi equation as a non-metric Euler equation

In this paper we present a geometric interpretation of the periodic Degasperis-Procesi equation as the geodesic flow of a right invariant symmetric linear connection on the diffeomorphism group of the circle. We also show that for any evolution in the family of $b$-equations there is neither gain nor loss of the spatial regularity of solutions. This in turn allows us to view the Degasperis-Procesi and the Camassa-Holm equation as an ODE on the Fr\'echet space of all smooth functions on the circle.Comment: 17 page

Synthetic long non-coding RNAs [SINEUPs] rescue defective gene expression in vivo

Non-coding RNAs provide additional regulatory layers to gene expression as well as the potential to being exploited as therapeutic tools. Non-coding RNA-based therapeutic approaches have been attempted in dominant diseases, however their use for treatment of genetic diseases caused by insufficient gene dosage is currently more challenging. SINEUPs are long antisense non-coding RNAs that up-regulate translation in mammalian cells in a gene-specific manner, although, so far evidence of SINEUP efficacy has only been demonstrated in in vitro systems. We now show that synthetic SINEUPs effectively and specifically increase protein levels of a gene of interest in vivo. We demonstrated that SINEUPs rescue haploinsufficient gene dosage in a medakafish model of a human disorder leading to amelioration of the disease phenotype. Our results demonstrate that SINEUPs act through mechanisms conserved among vertebrates and that SINEUP technology can be successfully applied in vivo as a new research and therapeutic tool for gene-specific up-regulation of endogenous functional proteins

Regulation of the Cardiac Na+/K+ ATPase by Phospholemman

Hansraj Dhayan, Rajender Kumar, Andreas Kukol, ‘Regulation of the Cardiac Na+/K+ ATPase by Phospholemman’, in Sajal Chakraborti, Naranjan Dhalla, eds., Regulation of Membrane Na+-K+ ATPase, (Switzerland: Springer, 2016), ISBN 978-3-319-24748-9, eISBN 978-3-319-24750-2.Peer reviewe

Methods to study splicing from high-throughput RNA Sequencing data

The development of novel high-throughput sequencing (HTS) methods for RNA (RNA-Seq) has provided a very powerful mean to study splicing under multiple conditions at unprecedented depth. However, the complexity of the information to be analyzed has turned this into a challenging task. In the last few years, a plethora of tools have been developed, allowing researchers to process RNA-Seq data to study the expression of isoforms and splicing events, and their relative changes under different conditions. We provide an overview of the methods available to study splicing from short RNA-Seq data. We group the methods according to the different questions they address: 1) Assignment of the sequencing reads to their likely gene of origin. This is addressed by methods that map reads to the genome and/or to the available gene annotations. 2) Recovering the sequence of splicing events and isoforms. This is addressed by transcript reconstruction and de novo assembly methods. 3) Quantification of events and isoforms. Either after reconstructing transcripts or using an annotation, many methods estimate the expression level or the relative usage of isoforms and/or events. 4) Providing an isoform or event view of differential splicing or expression. These include methods that compare relative event/isoform abundance or isoform expression across two or more conditions. 5) Visualizing splicing regulation. Various tools facilitate the visualization of the RNA-Seq data in the context of alternative splicing. In this review, we do not describe the specific mathematical models behind each method. Our aim is rather to provide an overview that could serve as an entry point for users who need to decide on a suitable tool for a specific analysis. We also attempt to propose a classification of the tools according to the operations they do, to facilitate the comparison and choice of methods.Comment: 31 pages, 1 figure, 9 tables. Small corrections adde

Identification of antisense long noncoding RNAs that function as SINEUPs in human cells

Mammalian genomes encode numerous natural antisense long noncoding RNAs (lncRNAs) that regulate gene expression. Recently, an antisense lncRNA to mouse Ubiquitin carboxyl-terminal hydrolase L1 (Uchl1) was reported to increase UCHL1 protein synthesis, representing a new functional class of lncRNAs, designated as SINEUPs, for SINE element-containing translation UP-regulators. Here, we show that an antisense lncRNA to the human protein phosphatase 1 regulatory subunit 12A (PPP1R12A), named as R12A-AS1, which overlaps with the 5' UTR and first coding exon of the PPP1R12A mRNA, functions as a SINEUP, increasing PPP1R12A protein translation in human cells. The SINEUP activity depends on the aforementioned sense-antisense interaction and a free right Alu monomer repeat element at the 3' end of R12A-AS1. In addition, we identify another human antisense lncRNA with SINEUP activity. Our results demonstrate for the first time that human natural antisense lncRNAs can up-regulate protein translation, suggesting that endogenous SINEUPs may be widespread and present in many mammalian species