Generalizations of Commutativity in Dihedral Groups

The probability that two elements commute in a non-Abelian finite group is at most 5 8 . We prove several generalizations of this result for dihedral groups. In particular, we give specific values for the probability that a product of an arbitrary number of dihedral group elements is equal to its reverse, and also for the probability that a product of three elements is equal to a permutation of itself or to a cyclic permutation of itself. We also show that for any r and n, there exists a dihedral group such that the probability that a product of n elements is equal to its reverse is r q for some q coprime to r, extending a known result

The Ophthalmic Experience: Unanticipated Primary Findings in the Era of Next Generation Sequencing

Next generation sequencing (NGS) technology, with the ability to sequence many genomic regions at once, can provide clinicians with increased information, in the form of more mutations detected. Discussions on broad testing technology have largely been focused on incidental findings, or unanticipated results related to diseases beyond the primary indication for testing. By examining multiple genes that could be responsible for the patient’s presentation, however, there is also the possibility of unexpected results that are related to the reason genetic testing was ordered. We present a case study where multiple potentially causative mutations were detected using NGS technology. This case raises questions of scientific uncertainty, and has important implications for medical management and secondary studies. Clinicians and genetic counselors should be aware of the potential for increased information to affect one’s understanding of genetic risk, and the pre‐ and post‐testing counseling process.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/147171/1/jgc40588.pd

Scotopic and Photopic Visual Thresholds and Spatial and Temporal Discrimination Evaluated by Behavior of Mice in a Water Maze †

Methods that allow specific manipulations of the mouse genome have made it possible to alter specific aspects of photoreceptor function within the mouse retina. Mice with photoreceptors that have altered photosensitivities and altered photoresponse kinetics are now available. Methods are needed that can show how those perturbations in photoreceptor response characteristics translate into perturbations in visual sensitivity and perception. We have adapted a previously described method to evaluate visual threshold, spatial discrimination and temporal discrimination in mice swimming in a water maze. In this report we describe the sensitivities of rod-mediated and cone-mediated vision using GNAT1–/–and GNAT2–/– mice. Cone-mediated vision is ˜10000 times less sensitive than rod-mediated vision in mice. We also demonstrate that mice can distinguish striped from solid objects in the water maze and that they can distinguish flickering from continuous illumination.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75706/1/j.1751-1097.2006.tb09804.x.pd

Horizontal compensatory eye movements in goldfish ( Carassius auratus )

1. Horizontal eye and head movements made by freely swimming goldfish have been recorded cinematographically and analyzed frame-by-frame.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47112/1/359_2004_Article_BF00696524.pd

Hereditary and Clinical Features of Retinitis Pigmentosa in Koreans

There has been no report about hereditary and clinical features of retinitis pigmentosa (RP) in Koreans. To evaluate these, data were collected from 365 RP patients including age, gender, visual acuity (VA), spherical equivalent (SE) of refractive errors, funduscopic findings, color vision test, visual field score (VFS) obtained from Goldmann perimetry, and the inheritance patterns from pedigrees. Simplex RP was the most common inheritance pattern (61.9%); followed by autosomal recessive RP (17.3%), autosomal dominant RP (12.1%) and X-linked recessive RP (8.8%). Myopia was the most common refractive errors (77.5%) including 16.1% of high myopia. The most common cataract type was posterior subcapsular cataract (25.8%). Observed retinal findings included changes of retinal pigment epithelium (88.8%), bony spicule-like pigmentation (79.7%), attenuation of retinal vessel (76.2%), waxy disc pallor (12.6%), golden ring around optic disc (2.2%), epiretinal membrane (0.8%) and cystoid macular edema (0.5%). Corrected VA and refractive errors did not show any significant difference between the inheritance patterns. VFS was significantly worse in autosomal recessive RP than in autosomal dominant RP. Color vision defect was noted in 66.1% on Hardy-Rand-Rittlers color vision test. In conclusion, Korean RP patients have the indigenous hereditary and clinical features as well as the ordinary ones

Autoantibodies against retinal proteins in paraneoplastic and autoimmune retinopathy

BACKGROUND: Autoimmune retinal degeneration may occur in patients who present with sudden or, less commonly, subacute loss of vision of retinal origin, associated with an abnormal ERG, through the action of autoantibodies against retinal proteins. Often the patients are initially diagnosed with or suspected of having a paraneoplastic retinopathy (PR), such as cancer-associated retinopathy (CAR). However, there is limited information on the occurrence, the specificity of autoantibodies in these patients, and their association with clinical symptoms. METHODS: Sera were obtained from 193 retinopathy patients who presented with clinical symptoms resembling PR or autoimmune retinopathy (AR), including sudden painless loss of vision, typically associated with visual field defects and photopsias, and abnormal rod and/or cone responses on the electroretinogram (ERG). Sera were tested for the presence of anti-retinal autoantibodies by Western blot analysis using proteins extracted from human retina and by immunohistochemistry. Autoantibody titers against recoverin and enolase were measured by ELISA. RESULTS: We identified a higher prevalence of anti-retinal autoantibodies in retinopathy patients. Ninety-one patients' sera (47.1%) showed autoantibodies of various specificities with a higher incidence of antibodies present in retinopathy patients diagnosed with cancer (33/52; 63.5%; p = 0.009) than in retinopathy patients without cancer (58/141; 41.1%). The average age of PR patients was 62.0 years, and that of AR patients was 55.9 years. Autoantibodies against recoverin (p23) were only present in the sera of PR patients, autoantibodies against unknown p35 were more common in patients with AR, while anti-enolase (anti-p46) autoantibodies were nearly equally distributed in the sera of patients with PR and those with AR. In the seropositive patients, the autoantibodies persisted over a long period of time – from months to years. A rebound in anti-recoverin autoantibody titer was found to be associated with exacerbations in visual symptoms but not in the recurrence of cancer. When compared to sera from healthy subjects, autoantibodies against retinal proteins from both groups of patients were cytotoxic to retinal cells, indicating their pathogenic potential. CONCLUSIONS: These studies showed that patients with sudden or subacute, unexplained loss of vision of retinal origin have anti-retinal antibodies in a broad range of specificity and indicate the need for autoantibody screening. Follow-up tests of antibody levels may be useful as a biomarker of disease activity associated with worsening of vision. Moreover, the heterogeneity in autoantibody specificity may explain the variation and complexity of clinical symptoms in retinopathy patients

Sudden acquired retinal degeneration syndrome (SARDS) â a review and proposed strategies toward a better understanding of pathogenesis, early diagnosis, and therapy

Sudden acquired retinal degeneration syndrome (SARDS) is one of the leading causes of currently incurable canine vision loss diagnosed by veterinary ophthalmologists. The disease is characterized by acute onset of blindness due to loss of photoreceptor function, extinguished electroretinogram with an initially normal appearing ocular fundus, and mydriatic pupils which are slowly responsive to bright white light, unresponsive to red, but responsive to blue light stimulation. In addition to blindness, the majority of affected dogs also show systemic abnormalities suggestive of hyperadrenocorticism, such as polyphagia with resulting obesity, polyuria, polydipsia, and a subclinical hepatopathy. The pathogenesis of SARDS is unknown, but neuroendocrine and autoimmune mechanisms have been suggested. Therapies that target these disease pathways have been proposed to reverse or prevent further vision loss in SARDSâ affected dogs, but these treatments are controversial. In November 2014, the American College of Veterinary Ophthalmologists' Vision for Animals Foundation organized and funded a Think Tank to review the current knowledge and recently proposed ideas about disease mechanisms and treatment of SARDS. These panel discussions resulted in recommendations for future research strategies toward a better understanding of pathogenesis, early diagnosis, and potential therapy for this condition.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/122446/1/vop12291.pd

Mutations in the gene PDE6C encoding the catalytic subunit of the cone photoreceptor phosphodiesterase in patients with achromatopsia

Biallelic PDE6C mutations are a known cause for rod monochromacy, better known as autosomal recessive achromatopsia (ACHM), and early‐onset cone photoreceptor dysfunction. PDE6C encodes the catalytic α′‐subunit of the cone photoreceptor phosphodiesterase, thereby constituting an essential part of the phototransduction cascade. Here, we present the results of a study comprising 176 genetically preselected patients who remained unsolved after Sanger sequencing of the most frequent genes accounting for ACHM, and were subsequently screened for exonic and splice site variants in PDE6C applying a targeted next generation sequencing approach. We were able to identify potentially pathogenic biallelic variants in 15 index cases. The mutation spectrum comprises 18 different alleles, 15 of which are novel. Our study significantly contributes to the mutation spectrum of PDE6C and allows for a realistic estimate of the prevalence of PDE6C mutations in ACHM since our entire ACHM cohort comprises 1,074 independent families.In a cohort of 176 genetically undiagnosed achromatopsia patients, we performed screening of the PDE6C gene and identified potentially pathogenic biallelic variants in 15 cases. Taking into account a previous screening approach, we calculate a prevalence of 2.4% for PDE6C mutations in our cohort, which is most probably representative for the Western population. As achromatopsia is in the focus of retinal gene therapy with four clinical trials ongoing, our study provides a valuable resource for putative gene therapy trials targeting PDE6C.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/146275/1/humu23606-sup-0001-SuppMat.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/146275/2/humu23606_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/146275/3/humu23606.pd