BDDC and FETI-DP under Minimalist Assumptions

The FETI-DP, BDDC and P-FETI-DP preconditioners are derived in a particulary simple abstract form. It is shown that their properties can be obtained from only on a very small set of algebraic assumptions. The presentation is purely algebraic and it does not use any particular definition of method components, such as substructures and coarse degrees of freedom. It is then shown that P-FETI-DP and BDDC are in fact the same. The FETI-DP and the BDDC preconditioned operators are of the same algebraic form, and the standard condition number bound carries over to arbitrary abstract operators of this form. The equality of eigenvalues of BDDC and FETI-DP also holds in the minimalist abstract setting. The abstract framework is explained on a standard substructuring example.Comment: 11 pages, 1 figure, also available at http://www-math.cudenver.edu/ccm/reports

Multispace and Multilevel BDDC

BDDC method is the most advanced method from the Balancing family of iterative substructuring methods for the solution of large systems of linear algebraic equations arising from discretization of elliptic boundary value problems. In the case of many substructures, solving the coarse problem exactly becomes a bottleneck. Since the coarse problem in BDDC has the same structure as the original problem, it is straightforward to apply the BDDC method recursively to solve the coarse problem only approximately. In this paper, we formulate a new family of abstract Multispace BDDC methods and give condition number bounds from the abstract additive Schwarz preconditioning theory. The Multilevel BDDC is then treated as a special case of the Multispace BDDC and abstract multilevel condition number bounds are given. The abstract bounds yield polylogarithmic condition number bounds for an arbitrary fixed number of levels and scalar elliptic problems discretized by finite elements in two and three spatial dimensions. Numerical experiments confirm the theory.Comment: 26 pages, 3 figures, 2 tables, 20 references. Formal changes onl

Search for a correlation between telomere length and severity of retinitis pigmentosa due to the dominant rhodopsin Pro23His mutation

Purpose: Great variation exists in the age of onset of symptoms and the severity of disease at a given age in patients with retinitis pigmentosa ( RP). The final pathway for this disease may involve apoptotic photoreceptor cell death. Telomere length is associated with biologic aging, senescence, and apoptosis. We evaluated whether the length of telomeres in leukocytes correlated with the severity of RP in patients with the Pro23His rhodopsin mutation who have shown marked heterogeneity in disease severity. Methods: We evaluated 122 patients with the Pro23His rhodopsin mutation. The patients' retinal function was stratified according to their 30-Hz cone electroretinogram (ERG). The length of telomeres in leukocytes was measured by the quantitative real time polymerase chain reaction (qRT-PCR) method in the 15 patients with the highest age-adjusted 30Hz ERG amplitudes and in the 15 patients with the lowest amplitudes. Results: Mean leukocyte telomere length was similar in the 15 patients with the highest cone ERG amplitudes (median: 0.40 units; interquartile range 0.36-0.56) and the 15 patients with the lowest cone amplitudes (median: 0.41 units; inter quartile range 0.34-0.64; p=0.95). Conclusions: We found no evidence for an association between telomere length and the severity of RP as monitored by the cone ERG in patients with the Pro23His rhodopsin mutation

Comprehensive Analysis of CRP, CFH Y402H and Environmental Risk Factors on Risk of Neovascular Age-Related Macular Degeneration

Purpose: To examine if the gene encoding C-reactive protein (CRP), a biomarker of inflammation, confers risk for neovascular age-related macular degeneration (AMD) in the presence of other modifiers of inflammation, including body mass index (BMI), diabetes, smoking, and complement factor H (CFH) Y402 genotype. Additionally we examined the degree to which CRP common variation was in linkage disequilibrium (LD) within our cohort. Methods: We ascertained 244 individuals from 104 families where at least one member had neovascular AMD, and a sibling had normal maculae and was past the age of the index patient’s diagnosis of neovascular AMD. We employed a direct sequencing approach to analyze the 5′-promoter region as well as the entire coding region and the 3′-untranslated region of the CRP gene. CFH Y402 genotype data was available for all participants. Lifestyle and medical factors were obtained via administration of a standardized questionnaire. The family-based association test, haplotype analysis, McNemar’s test, and conditional logistic regression were used to determine significant associations and interactions. Haploview was used to calculate the degree of LD (r2) between all CRP variants identified. Results: Six single nucleotide polymorphisms (SNPs; rs3091244, rs1417938, rs1800947, rs1130864, rs1205, and rs3093068) comprised one haplotype block of which only rs1130864 and rs1417938 were in high LD (r2=0.94). SNP rs3093068 was in LD but less so with rs3093059 (r2=0.83), which is not part of the haplotype block. Six SNPs made up six different haplotypes with ≥ 5% frequency, none of which were significantly associated with AMD risk. No statistically significant association was detected between any of the nine common variants in CRP and neovascular AMD when considering disease status alone or when controlling for smoking exposure, BMI, diabetes, or CFH genotype. Significant interactions were not found between CRP genotypes and any of the risk factors studied. No novel CRP variation was identified. Conclusions: We provide evidence that if elevated serum/plasma levels of CRP are associated with neovascular AMD, it is likely not due to genetic variation within CRP, but likely due to variations in some other genetic as well as epidemiological factors

Rpgrip1 is required for rod outer segment development and ciliary protein trafficking in zebrafish

The authors would like to thank the Royal Society of London, the National Eye Research Centre, the Visual Research Trust, Fight for Sight, the W.H. Ross Foundation, the Rosetrees Trust, and the Glasgow Children’s Hospital Charity for supporting this work. This work was also supported by the Deanship of Scientific Research at King Saud University for funding this research (Research Project) grant number ‘RGP – VPP – 219’.Mutations in the RPGR-interacting protein 1 (RPGRIP1) gene cause recessive Leber congenital amaurosis (LCA), juvenile retinitis pigmentosa (RP) and cone-rod dystrophy. RPGRIP1 interacts with other retinal disease-causing proteins and has been proposed to have a role in ciliary protein transport; however, its function remains elusive. Here, we describe a new zebrafish model carrying a nonsense mutation in the rpgrip1 gene. Rpgrip1homozygous mutants do not form rod outer segments and display mislocalization of rhodopsin, suggesting a role for RPGRIP1 in rhodopsin-bearing vesicle trafficking. Furthermore, Rab8, the key regulator of rhodopsin ciliary trafficking, was mislocalized in photoreceptor cells of rpgrip1 mutants. The degeneration of rod cells is early onset, followed by the death of cone cells. These phenotypes are similar to that observed in LCA and juvenile RP patients. Our data indicate RPGRIP1 is necessary for rod outer segment development through regulating ciliary protein trafficking. The rpgrip1 mutant zebrafish may provide a platform for developing therapeutic treatments for RP patients.Publisher PDFPeer reviewe

Rescue of Photoreceptor Degeneration by Curcumin in Transgenic Rats with P23H Rhodopsin Mutation

The P23H mutation in the rhodopsin gene causes rhodopsin misfolding, altered trafficking and formation of insoluble aggregates leading to photoreceptor degeneration and autosomal dominant retinitis pigmentosa (RP). There are no effective therapies to treat this condition. Compounds that enhance dissociation of protein aggregates may be of value in developing new treatments for such diseases. Anti-protein aggregating activity of curcumin has been reported earlier. In this study we present that treatment of COS-7 cells expressing mutant rhodopsin with curcumin results in dissociation of mutant protein aggregates and decreases endoplasmic reticulum stress. Furthermore we demonstrate that administration of curcumin to P23H-rhodopsin transgenic rats improves retinal morphology, physiology, gene expression and localization of rhodopsin. Our findings indicate that supplementation of curcumin improves retinal structure and function in P23H-rhodopsin transgenic rats. This data also suggest that curcumin may serve as a potential therapeutic agent in treating RP due to the P23H rhodopsin mutation and perhaps other degenerative diseases caused by protein trafficking defects

\u3cem\u3eRPGRIP1\u3c/em\u3e and Cone-Rod Dystrophy in Dogs

Cone–rod dystrophies (crd) represent a group of progressive inherited blinding diseases characterized by primary dysfunction and loss of cone photoreceptors accompanying or preceding rod death. Recessive crd type 1 was described in dogs associated with an RPGRIP1 exon 2 mutation, but with lack of complete concordance between genotype and phenotype. This review highlights role of the RPGRIP1, a component of complex protein networks, and its function in the primary cilium, and discusses the potential mechanisms of genotype–phenotype discordance observed in dogs with the RPGRIP1 mutation

Microglia activation in a model of retinal degeneration and TUDCA neuroprotective effects

Background: Retinitis pigmentosa is a heterogeneous group of inherited neurodegenerative retinal disorders characterized by a progressive peripheral vision loss and night vision difficulties, subsequently leading to central vision impairment. Chronic microglia activation is associated with various neurodegenerative diseases including retinitis pigmentosa. The objective of this study was to quantify microglia activation in the retina of P23H rats, an animal model of retinitis pigmentosa, and to evaluate the therapeutic effects of TUDCA (tauroursodeoxycholic acid), which has been described as a neuroprotective compound. Methods: For this study, homozygous P23H line 3 and Sprague-Dawley (SD) rats were injected weekly with TUDCA (500 mg/kg, ip) or vehicle (saline) from 20 days to 4 months old. Vertical retinal sections and whole-mount retinas were immunostained for specific markers of microglial cells (anti-CD11b, anti-Iba1 and anti-MHC-II). Microglial cell morphology was analyzed and the number of retinal microglial was quantified. Results: Microglial cells in the SD rat retinas were arranged in regular mosaics homogenously distributed within the plexiform and ganglion cell layers. In the P23H rat retina, microglial cells increased in number in all layers compared with control SD rat retinas, preserving the regular mosaic distribution. In addition, a large number of amoeboid CD11b-positive cells were observed in the P23H rat retina, even in the subretinal space. Retinas of TUDCA-treated P23H animals exhibited lower microglial cell number in all layers and absence of microglial cells in the subretinal space. Conclusions: These results report novel TUDCA anti-inflammatory actions, with potential therapeutic implications for neurodegenerative diseases, including retinitis pigmentosa.This research was supported by grants from the Spanish Ministry of Economy and Competitiveness-FEDER (BFU2012-36845), Instituto de Salud Carlos III (RETICS RD12/0034/0010), Organización Nacional de Ciegos Españoles (ONCE), FUNDALUCE, Asociación Retina Asturias and Fundación Jesús de Gangoiti