Common fixed points and invariant approximation of R-subweakly commuting maps in convex metric spaces

Sufficient conditions for the existence of a common fixed point of R-subweakly commuting mappings are established within the framework of a convex metric space. As applications, we obtain various results on the best approximation for this class of mappings generalizing the results known from the literature.Встановлено достатні умови існування спільної нерухомої точки R-субслабко комутуючих відображень у рамках опуклого метричного простору. Як застосування, одержано різні результати щодо найкращих наближень для згаданого класу відображень, які узагальнюють інші відомі з літератури результати

Common fixed-point theorems for nonlinear weakly contractive mappings

Some common fixed-point results for mappings satisfying a nonlinear weak contraction condition within the framework of ordered metric spaces are obtained. The accumulated results generalize and extend several comparable results well-known from the literature.Отримано дєякі спільні теореми про нерухому точку для відображень, що задовольняють нелінійну слабкостискальну умову в рамках упорядкованих метричних просторів. Отримані результати узагальнюють та розширюють декілька порівняльних результатів, відомих із літературних джерел

Fixed point results in ordered metric spaces for rational type expressions with auxiliary functions

AbstractIn this paper, we establish some fixed point results for mappings involving (ϕ,ψ)-rational type contractions in the framework of metric spaces endowed with a partial order. These results generalize and extend some known results in the literature. Four illustrative examples are given

Common fixed-point theorems for nonlinear weakly contractive mappings

Some common fixed-point results for mappings satisfying a nonlinear weak contraction condition within the framework of ordered metric spaces are obtained. The accumulated results generalize and extend several comparable results well-known from the literature.http://link.springer.com/journal/112532015-09-30hj201

MutLα heterodimers modify the molecular phenotype of Friedreich ataxia

This article has been made available through the Brunel Open Access Publishing Fund.Background: Friedreich ataxia (FRDA), the most common autosomal recessive ataxia disorder, is caused by a dynamic GAA repeat expansion mutation within intron 1 of FXN gene, resulting in down-regulation of frataxin expression. Studies of cell and mouse models have revealed a role for the mismatch repair (MMR) MutS-heterodimer complexes and the PMS2 component of the MutLα complex in the dynamics of intergenerational and somatic GAA repeat expansions: MSH2, MSH3 and MSH6 promote GAA repeat expansions, while PMS2 inhibits GAA repeat expansions. Methodology/Principal Findings: To determine the potential role of the other component of the MutLα complex, MLH1, in GAA repeat instability in FRDA, we have analyzed intergenerational and somatic GAA repeat expansions from FXN transgenic mice that have been crossed with Mlh1 deficient mice. We find that loss of Mlh1 activity reduces both intergenerational and somatic GAA repeat expansions. However, we also find that loss of either Mlh1 or Pms2 reduces FXN transcription, suggesting different mechanisms of action for Mlh1 and Pms2 on GAA repeat expansion dynamics and regulation of FXN transcription. Conclusions/Significance: Both MutLα components, PMS2 and MLH1, have now been shown to modify the molecular phenotype of FRDA. We propose that upregulation of MLH1 or PMS2 could be potential FRDA therapeutic approaches to increase FXN transcription. © 2014 Ezzatizadeh et al.This article has been made available through the Brunel Open Access Publishing Fund

Generation and characterisation of Friedreich ataxia YG8R mouse fibroblast and neural stem cell models

This article has been made available through the Brunel Open Access Publishing Fund.Background: Friedreich ataxia (FRDA) is an autosomal recessive neurodegenerative disease caused by GAA repeat expansion in the first intron of the FXN gene, which encodes frataxin, an essential mitochondrial protein. To further characterise the molecular abnormalities associated with FRDA pathogenesis and to hasten drug screening, the development and use of animal and cellular models is considered essential. Studies of lower organisms have already contributed to understanding FRDA disease pathology, but mammalian cells are more related to FRDA patient cells in physiological terms. Methodology/Principal Findings: We have generated fibroblast cells and neural stem cells (NSCs) from control Y47R mice (9 GAA repeats) and GAA repeat expansion YG8R mice (190+120 GAA repeats). We then differentiated the NSCs in to neurons, oligodendrocytes and astrocytes as confirmed by immunocytochemical analysis of cell specific markers. The three YG8R mouse cell types (fibroblasts, NSCs and differentiated NSCs) exhibit GAA repeat stability, together with reduced expression of frataxin and reduced aconitase activity compared to control Y47R cells. Furthermore, YG8R cells also show increased sensitivity to oxidative stress and downregulation of Pgc-1α and antioxidant gene expression levels, especially Sod2. We also analysed various DNA mismatch repair (MMR) gene expression levels and found that YG8R cells displayed significant reduction in expression of several MMR genes, which may contribute to the GAA repeat stability. Conclusions/Significance: We describe the first fibroblast and NSC models from YG8R FRDA mice and we confirm that the NSCs can be differentiated into neurons and glia. These novel FRDA mouse cell models, which exhibit a FRDA-like cellular and molecular phenotype, will be valuable resources to further study FRDA molecular pathogenesis. They will also provide very useful tools for preclinical testing of frataxin-increasing compounds for FRDA drug therapy, for gene therapy, and as a source of cells for cell therapy testing in FRDA mice. © 2014 Sandi et al