Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps

Coarse spaces are instrumental in obtaining scalability for domain decomposition methods for partial differential equations (PDEs). However, it is known that most popular choices of coarse spaces perform rather weakly in the presence of heterogeneities in the PDE coefficients, especially for systems of PDEs. Here, we introduce in a variational setting a new coarse space that is robust even when there are such heterogeneities. We achieve this by solving local generalized eigenvalue problems in the overlaps of subdomains that isolate the terms responsible for slow convergence. We prove a general theoretical result that rigorously establishes the robustness of the new coarse space and give some numerical examples on two and three dimensional heterogeneous PDEs and systems of PDEs that confirm this property

A Unified Analysis of Balancing Domain Decomposition by Constraints for Discontinuous Galerkin Discretizations

The BDDC algorithm is extended to a large class of discontinuous Galerkin (DG) discretizations of second order elliptic problems. An estimate of C(1 + log(H/h))2 is obtained for the condition number of the preconditioned system where C is a constant independent of h or H or large jumps in the coefficient of the problem. Numerical simulations are presented which confirm the theoretical results. A key component for the development and analysis of the BDDC algorithm is a novel perspective presenting the DG discretization as the sum of element-wise “local” bilinear forms. The element-wise perspective allows for a simple unified analysis of a variety of DG methods and leads naturally to the appropriate choice for the subdomain-wise local bilinear forms. Additionally, this new perspective enables a connection to be drawn between the DG discretization and a related continuous finite element discretization to simplify the analysis of the BDDC algorithm.Boeing CompanyMassachusetts Institute of Technology (Zakhartchenko Fellowship

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

\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

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

Three novel and the common Arg677Ter RP1 protein truncating mutations causing autosomal dominant retinitis pigmentosa in a Spanish population

BACKGROUND: Retinitis pigmentosa (RP), a clinically and genetically heterogeneous group of retinal degeneration disorders affecting the photoreceptor cells, is one of the leading causes of genetic blindness. Mutations in the photoreceptor-specific gene RP1 account for 3–10% of cases of autosomal dominant RP (adRP). Most of these mutations are clustered in a 500 bp region of exon 4 of RP1. METHODS: Denaturing gradient gel electrophoresis (DGGE) analysis and direct genomic sequencing were used to evaluate the 5' coding region of exon 4 of the RP1 gene for mutations in 150 unrelated index adRP patients. Ophthalmic and electrophysiological examination of RP patients and relatives according to pre-existing protocols were carried out. RESULTS: Three novel disease-causing mutations in RP1 were detected: Q686X, K705fsX712 and K722fsX737, predicting truncated proteins. One novel missense mutation, Thr752Met, was detected in one family but the mutation does not co-segregate in the family, thereby excluding this amino acid variation in the protein as a cause of the disease. We found the Arg677Ter mutation, previously reported in other populations, in two independent families, confirming that this mutation is also present in a Spanish population. CONCLUSION: Most of the mutations reported in the RP1 gene associated with adRP are expected to encode mutant truncated proteins that are approximately one third or half of the size of wild type protein. Patients with mutations in RP1 showed mild RP with variability in phenotype severity. We also observed several cases of non-penetrant mutations

Bax-Induced Apoptosis in Leber's Congenital Amaurosis: A Dual Role in Rod and Cone Degeneration

Pathogenesis in the Rpe65−/− mouse model of Leber's congenital amaurosis (LCA) is characterized by a slow and progressive degeneration of the rod photoreceptors. On the opposite, cones degenerate rapidly at early ages. Retinal degeneration in Rpe65−/− mice, showing a null mutation in the gene encoding the retinal pigment epithelium 65-kDa protein (Rpe65), was previously reported to depend on continuous activation of a residual transduction cascade by unliganded opsin. However, the mechanisms of apoptotic signals triggered by abnormal phototransduction remain elusive. We previously reported that activation of a Bcl-2-dependent pathway was associated with apoptosis of rod photoreceptors in Rpe65−/− mice during the course of the disease. In this study we first assessed whether activation of Bcl-2-mediated apoptotic pathway was dependent on constitutive activation of the visual cascade through opsin apoprotein. We then challenged the direct role of pro-apoptotic Bax protein in triggering apoptosis of rod and cone photoreceptors

Detection of Variants in 15 Genes in 87 Unrelated Chinese Patients with Leber Congenital Amaurosis

BACKGROUND: Leber congenital amaurosis (LCA) is the earliest onset and most severe form of hereditary retinal dystrophy. So far, full spectrum of variations in the 15 genes known to cause LCA has not been systemically evaluated in East Asians. Therefore, we performed comprehensive detection of variants in these 15 genes in 87 unrelated Han Chinese patients with LCA. METHODOLOGY/PRINCIPAL FINDINGS: The 51 most frequently mutated exons and introns in the 15 genes were selected for an initial scan using cycle sequencing. All the remaining exons in 11 of the 15 genes were subsequently sequenced. Fifty-three different variants were identified in 44 of the 87 patients (50.6%), involving 78 of the 88 alleles (11 homozygous and 56 heterozygous variants). Of the 53 variants, 35 (66%) were novel pathogenic mutations. In these Chinese patients, variants in GUCY2D are the most common cause of LCA (16.1% cases), followed by CRB1 (11.5%), RPGRIP1 (8%), RPE65 (5.7%), SPATA7 (4.6%), CEP290 (4.6%), CRX (3.4%), LCA5 (2.3%), MERTK (2.3%), AIPL1 (1.1%), and RDH12 (1.1%). This differs from the variation spectrum described in other populations. An initial scan of 55 of 215 PCR amplicons, including 214 exons and 1 intron, detected 83.3% (65/78) of the mutant alleles ultimately found in these 87 patients. In addition, sequencing only 9 exons would detect over 50% of the identified variants and require less than 5% of the labor and cost of comprehensive sequencing for all exons. CONCLUSIONS/SIGNIFICANCE: Our results suggest that specific difference in the variation spectrum found in LCA patients from the Han Chinese and other populations are related by ethnicity. Sequencing exons in order of decreasing risk is a cost-effective way to identify causative mutations responsible for LCA, especially in the context of genetic counseling for individual patients in a clinical setting