On the rate of quantum ergodicity in Euclidean billiards

For a large class of quantized ergodic flows the quantum ergodicity theorem due to Shnirelman, Zelditch, Colin de Verdi\`ere and others states that almost all eigenfunctions become equidistributed in the semiclassical limit. In this work we first give a short introduction to the formulation of the quantum ergodicity theorem for general observables in terms of pseudodifferential operators and show that it is equivalent to the semiclassical eigenfunction hypothesis for the Wigner function in the case of ergodic systems. Of great importance is the rate by which the quantum mechanical expectation values of an observable tend to their mean value. This is studied numerically for three Euclidean billiards (stadium, cosine and cardioid billiard) using up to 6000 eigenfunctions. We find that in configuration space the rate of quantum ergodicity is strongly influenced by localized eigenfunctions like bouncing ball modes or scarred eigenfunctions. We give a detailed discussion and explanation of these effects using a simple but powerful model. For the rate of quantum ergodicity in momentum space we observe a slower decay. We also study the suitably normalized fluctuations of the expectation values around their mean, and find good agreement with a Gaussian distribution.Comment: 40 pages, LaTeX2e. This version does not contain any figures. A version with all figures can be obtained from http://www.physik.uni-ulm.de/theo/qc/ (File: http://www.physik.uni-ulm.de/theo/qc/ulm-tp/tp97-8.ps.gz) In case of any problems contact Arnd B\"acker (e-mail: [email protected]) or Roman Schubert (e-mail: [email protected]

The Diagnostic Utility of Anti-cyclic Citrullinated Peptide Antibodies, Matrix Metalloproteinase-3, Rheumatoid Factor, Erythrocyte Sedimentation Rate, and C-reactive Protein in Patients with Erosive and Non-erosive Rheumatoid Arthritis

Objective: To compare the diagnostic utility of laboratory variables, including matrix metalloproteinase-3 (MMP-3), anti-cyclic citrullinated peptide (CCP) antibodies, rheumatoid factor (RF), erythrocyte sedimentation rate (ESR), and C-reactive protein (CRP) in patients with erosive and non-erosive rheumatoid arthritis (RA)

Autoantibody Epitope Spreading in the Pre-Clinical Phase Predicts Progression to Rheumatoid Arthritis

Rheumatoid arthritis (RA) is a prototypical autoimmune arthritis affecting nearly 1% of the world population and is a significant cause of worldwide disability. Though prior studies have demonstrated the appearance of RA-related autoantibodies years before the onset of clinical RA, the pattern of immunologic events preceding the development of RA remains unclear. To characterize the evolution of the autoantibody response in the preclinical phase of RA, we used a novel multiplex autoantigen array to evaluate development of the anti-citrullinated protein antibodies (ACPA) and to determine if epitope spread correlates with rise in serum cytokines and imminent onset of clinical RA. To do so, we utilized a cohort of 81 patients with clinical RA for whom stored serum was available from 1–12 years prior to disease onset. We evaluated the accumulation of ACPA subtypes over time and correlated this accumulation with elevations in serum cytokines. We then used logistic regression to identify a profile of biomarkers which predicts the imminent onset of clinical RA (defined as within 2 years of testing). We observed a time-dependent expansion of ACPA specificity with the number of ACPA subtypes. At the earliest timepoints, we found autoantibodies targeting several innate immune ligands including citrullinated histones, fibrinogen, and biglycan, thus providing insights into the earliest autoantigen targets and potential mechanisms underlying the onset and development of autoimmunity in RA. Additionally, expansion of the ACPA response strongly predicted elevations in many inflammatory cytokines including TNF-α, IL-6, IL-12p70, and IFN-γ. Thus, we observe that the preclinical phase of RA is characterized by an accumulation of multiple autoantibody specificities reflecting the process of epitope spread. Epitope expansion is closely correlated with the appearance of preclinical inflammation, and we identify a biomarker profile including autoantibodies and cytokines which predicts the imminent onset of clinical arthritis

The association of anti-CCP antibodies with disease activity in rheumatoid arthritis

Antibodies to citrullinated proteins have been described in patients with rheumatoid arthritis (RA) and these appear to be the most specific markers of the disease. Our objective was to determine the frequency of antibodies to cyclic citrullinated peptides (CCPs) in patients with RA and the association of anti-CCP antibodies with disease activity, radiological erosions and HLA DR genotype. Forty patients with RA and 38 patients with fibromyalgia were included in this study. Serum samples were collected from both patient groups with RA and fibromyalgia. Anti-CCP was measured by the corresponding enzyme-linked immunosorbent assay. Additionally, erythrocyte sedimentation rate (ESR), C-reactive protein (CRP), rheumatoid factor (RF), disease activity score (DAS), visual analog scala (VAS), HLA genotype and radiographic information were determined in patients with RA. The rate of sensitivity and specificity of anti-CCP reactivity for the diagnosis RA were measured (sensitivity 50%, specificity100%). There is no significant difference between anti-CCP (+) and anti-CCP (−) RA patients for DAS28, VAS, ESR, CRP, disease duration, HLA genotype, and radiological assessment of hand. However, there was a significant difference between anti-CCP (+) and anti-CCP (−) RA patients for RF and the radiological assessment of left and right wrists (respectively, P < 0.05, P = 0.04, P = 0.01). There was no significant correlation between anti-CCP antibody and ESR, CRP, VAS, DAS 28 or radiological assessment. A small but significant correlation was found between RF and anti-CCP antibody (P = 0.02, r = 0.35)

Natural history of limb girdle muscular dystrophy R9 over 6 years: searching for trial endpoints

OBJECTIVE: Limb girdle muscular dystrophy type R9 (LGMD R9) is an autosomal recessive muscle disease for which there is currently no causative treatment. The development of putative therapies requires sensitive outcome measures for clinical trials in this slowly progressing condition. This study extends functional assessments and MRI muscle fat fraction measurements in an LGMD R9 cohort across 6 years. METHODS: Twenty‐three participants with LGMD R9, previously assessed over a 1‐year period, were re‐enrolled at 6 years. Standardized functional assessments were performed including: myometry, timed tests, and spirometry testing. Quantitative MRI was used to measure fat fraction in lower limb skeletal muscle groups. RESULTS: At 6 years, all 14 muscle groups assessed demonstrated significant increases in fat fraction, compared to eight groups in the 1‐year follow‐up study. In direct contrast to the 1‐year follow‐up, the 6‐min walk test, 10‐m walk or run, timed up and go, stair ascend, stair descend and chair rise demonstrated significant decline. Among the functional tests, only FVC significantly declined over both the 1‐ and 6‐year studies. INTERPRETATION: These results further support fat fraction measurements as a primary outcome measure alongside functional assessments. The most appropriate individual muscles are the vastus lateralis, gracilis, sartorius, and gastrocnemii. Using composite groups of lower leg muscles, thigh muscles, or triceps surae, yielded high standardized response means (SRMs). Over 6 years, quantitative fat fraction assessment demonstrated higher SRM values than seen in functional tests suggesting greater responsiveness to disease progression

Natural history of limb girdle muscular dystrophy R9 over 6 years: searching for trial endpoints

OBJECTIVE: Limb girdle muscular dystrophy type R9 (LGMD R9) is an autosomal recessive muscle disease for which there is currently no causative treatment. The development of putative therapies requires sensitive outcome measures for clinical trials in this slowly progressing condition. This study extends functional assessments and MRI muscle fat fraction measurements in an LGMD R9 cohort across 6 years. METHODS: Twenty‐three participants with LGMD R9, previously assessed over a 1‐year period, were re‐enrolled at 6 years. Standardized functional assessments were performed including: myometry, timed tests, and spirometry testing. Quantitative MRI was used to measure fat fraction in lower limb skeletal muscle groups. RESULTS: At 6 years, all 14 muscle groups assessed demonstrated significant increases in fat fraction, compared to eight groups in the 1‐year follow‐up study. In direct contrast to the 1‐year follow‐up, the 6‐min walk test, 10‐m walk or run, timed up and go, stair ascend, stair descend and chair rise demonstrated significant decline. Among the functional tests, only FVC significantly declined over both the 1‐ and 6‐year studies. INTERPRETATION: These results further support fat fraction measurements as a primary outcome measure alongside functional assessments. The most appropriate individual muscles are the vastus lateralis, gracilis, sartorius, and gastrocnemii. Using composite groups of lower leg muscles, thigh muscles, or triceps surae, yielded high standardized response means (SRMs). Over 6 years, quantitative fat fraction assessment demonstrated higher SRM values than seen in functional tests suggesting greater responsiveness to disease progression

A New Fluorescence-Based Method Identifies Protein Phosphatases Regulating Lipid Droplet Metabolism

In virtually every cell, neutral lipids are stored in cytoplasmic structures called lipid droplets (LDs) and also referred to as lipid bodies or lipid particles. We developed a rapid high-throughput assay based on the recovery of quenched BODIPY-fluorescence that allows to quantify lipid droplets. The method was validated by monitoring lipid droplet turnover during growth of a yeast culture and by screening a group of strains deleted in genes known to be involved in lipid metabolism. In both tests, the fluorimetric assay showed high sensitivity and good agreement with previously reported data using microscopy. We used this method for high-throughput identification of protein phosphatases involved in lipid droplet metabolism. From 65 yeast knockout strains encoding protein phosphatases and its regulatory subunits, 13 strains revealed to have abnormal levels of lipid droplets, 10 of them having high lipid droplet content. Strains deleted for type I protein phosphatases and related regulators (ppz2, gac1, bni4), type 2A phosphatase and its related regulator (pph21 and sap185), type 2C protein phosphatases (ptc1, ptc4, ptc7) and dual phosphatases (pps1, msg5) were catalogued as high-lipid droplet content strains. Only reg1, a targeting subunit of the type 1 phosphatase Glc7p, and members of the nutrient-sensitive TOR pathway (sit4 and the regulatory subunit sap190) were catalogued as low-lipid droplet content strains, which were studied further. We show that Snf1, the homologue of the mammalian AMP-activated kinase, is constitutively phosphorylated (hyperactive) in sit4 and sap190 strains leading to a reduction of acetyl-CoA carboxylase activity. In conclusion, our fast and highly sensitive method permitted us to catalogue protein phosphatases involved in the regulation of LD metabolism and present evidence indicating that the TOR pathway and the SNF1/AMPK pathway are connected through the Sit4p-Sap190p pair in the control of lipid droplet biogenesis

Genetics of rheumatoid arthritis contributes to biology and drug discovery

A major challenge in human genetics is to devise a systematic strategy to integrate disease-associated variants with diverse genomic and biological datasets to provide insight into disease pathogenesis and guide drug discovery for complex traits such as rheumatoid arthritis (RA)1. Here, we performed a genome-wide association study (GWAS) meta-analysis in a total of >100,000 subjects of European and Asian ancestries (29,880 RA cases and 73,758 controls), by evaluating ~10 million single nucleotide polymorphisms (SNPs). We discovered 42 novel RA risk loci at a genome-wide level of significance, bringing the total to 1012–4. We devised an in-silico pipeline using established bioinformatics methods based on functional annotation5, cis-acting expression quantitative trait loci (cis-eQTL)6, and pathway analyses7–9 – as well as novel methods based on genetic overlap with human primary immunodeficiency (PID), hematological cancer somatic mutations and knock-out mouse phenotypes – to identify 98 biological candidate genes at these 101 risk loci. We demonstrate that these genes are the targets of approved therapies for RA, and further suggest that drugs approved for other indications may be repurposed for the treatment of RA. Together, this comprehensive genetic study sheds light on fundamental genes, pathways and cell types that contribute to RA pathogenesis, and provides empirical evidence that the genetics of RA can provide important information for drug discovery