On 1-factorizations of Bipartite Kneser Graphs

It is a challenging open problem to construct an explicit 1-factorization of the bipartite Kneser graph $H(v,t)$, which contains as vertices all $t$-element and $(v-t)$-element subsets of $[v]:=\{1,\ldots,v\}$ and an edge between any two vertices when one is a subset of the other. In this paper, we propose a new framework for designing such 1-factorizations, by which we solve a nontrivial case where $t=2$ and $v$ is an odd prime power. We also revisit two classic constructions for the case $v=2t+1$ --- the \emph{lexical factorization} and \emph{modular factorization}. We provide their simplified definitions and study their inner structures. As a result, an optimal algorithm is designed for computing the lexical factorizations. (An analogous algorithm for the modular factorization is trivial.)Comment: We design the first explicit 1-factorization of H(2,q), where q is a odd prime powe

Sparse Kneser graphs are Hamiltonian

For integers k≥1 and n≥2k+1, the Kneser graph K(n,k) is the graph whose vertices are the k-element subsets of {1,…,n} and whose edges connect pairs of subsets that are disjoint. The Kneser graphs of the form K(2k+1,k) are also known as the odd graphs. We settle an old problem due to Meredith, Lloyd, and Biggs from the 1970s, proving that for every k≥3, the odd graph K(2k+1,k) has a Hamilton cycle. This and a known conditional result due to Johnson imply that all Kneser graphs of the form K(2k+2a,k) with k≥3 and a≥0 have a Hamilton cycle. We also prove that K(2k+1,k) has at least 22k−6 distinct Hamilton cycles for k≥6. Our proofs are based on a reduction of the Hamiltonicity problem in the odd graph to the problem of finding a spanning tree in a suitably defined hypergraph on Dyck words

Tissue Clearing and Deep Imaging of the Kidney Using Confocal and Two-Photon Microscopy

Microscopic and macroscopic evaluation of biological tissues in three dimensions is becoming increasingly popular. This trend is coincident with the emergence of numerous tissue clearing strategies, and advancements in confocal and two-photon microscopy, enabling the study of intact organs and systems down to cellular and sub-cellular resolution. In this chapter, we describe a wholemount immunofluorescence technique for labeling structures in renal tissue. This technique combined with solvent-based tissue clearing and confocal imaging, with or without two-photon excitation, provides greater structural information than traditional sectioning and staining alone. Given the addition of paraffin embedding to our method, this hybrid protocol offers a powerful approach to combine confocal or two-photon findings with histological and further immunofluorescent analysis within the same tissue

Photoactivatable drugs for nicotinic optopharmacology

Photoactivatable pharmacological agents have revolutionized neuroscience, but the palette of available compounds is limited. We describe a general method for caging tertiary amines by using a stable quaternary ammonium linkage that elicits a red shift in the activation wavelength. We prepared a photoactivatable nicotine (PA-Nic), uncageable via one- or two-photon excitation, that is useful to study nicotinic acetylcholine receptors (nAChRs) in different experimental preparations and spatiotemporal scales

Bayesian Model Selection Applied to the Analysis of Fluorescence Correlation Spectroscopy Data of Fluorescent Proteins in Vitro and in Vivo

Fluorescence correlation spectroscopy (FCS) is a powerful technique to investigate molecular dynamics with single molecule sensitivity. In particular, in the life sciences it has found widespread application using fluorescent proteins as molecularly specific labels. However, FCS data analysis and interpretation using fluorescent proteins remains challenging due to typically low signal-to-noise ratio of FCS data and correlated noise in autocorrelated data sets. As a result, naive fitting procedures that ignore these important issues typically provide similarly good fits for multiple competing models without clear distinction of which model is preferred given the signal-to-noise ratio present in the data. Recently, we introduced a Bayesian model selection procedure to overcome this issue with FCS data analysis. The method accounts for the highly correlated noise that is present in FCS data sets and additionally penalizes model complexity to prevent over interpretation of FCS data. Here, we apply this procedure to evaluate FCS data from fluorescent proteins assayed in vitro and in vivo. Consistent with previous work, we demonstrate that model selection is strongly dependent on the signal-to-noise ratio of the measurement, namely, excitation intensity and measurement time, and is sensitive to saturation artifacts. Under fixed, low intensity excitation conditions, physical transport models can unambiguously be identified. However, at excitation intensities that are considered moderate in many studies, unwanted artifacts are introduced that result in nonphysical models to be preferred. We also determined the appropriate fitting models of a GFP tagged secreted signaling protein, Wnt3, in live zebrafish embryos, which is necessary for the investigation of Wnt3 expression and secretion in development. Bayes model selection therefore provides a robust procedure to determine appropriate transport and photophysical models for fluorescent proteins when appropriate models are provided, to help detect and eliminate experimental artifacts in solution, cells, and in living organisms.National Science Foundation (U.S.). Physics of Living Systems ProgramNational Institute of Mental Health (U.S.) (Award U01MH106011

Cognitive decline in Huntington's disease expansion gene carriers

BACKGROUND: In Huntington's Disease (HD) cognitive decline can occur before unequivocal motor signs become apparent. As cognitive decline often starts early in the course of the disease and has a progressive nature over time, cognition can be regarded as a key target for symptomatic treatment. The specific progressive profile of cognitive decline over time is unknown. OBJECTIVE: The aim of this study is to quantify the progression of cognitive decline across all HD stages, from pre-motormanifest to advanced HD, and to investigate if CAG length mediates cognitive decline. METHODS: In the European REGISTRY study 2669 HD expansion gene carriers underwent annual cognitive assessment. General linear mixed models were used to model the cognitive decline for each cognitive task across all disease stages. Additionally, a model was developed to evaluate the cognitive decline based on CAG length and age rather than disease stage. RESULTS: There was significant cognitive decline on all administered tasks throughout pre-motormanifest (close to estimated disease onset) participants and the subsequent motormanifest participants from stage 1 to stage 4. Performance on the Stroop Word and Stroop Color tests additionally declined significantly across the two pre-motormanifest groups: far and close to estimated disease onset. The evaluation of cognition performance in relation to CAG length and age revealed a more rapid cognitive decline in participants with longer CAG length than participants with shorter CAG length over time. CONCLUSION: Cognitive performance already shows decline in pre-motormanifest HD gene expansion carriers and gradually worsens to late stage HD. HD gene expansion carriers with certain CAG length have their own cognitive profile, i.e., longer CAG length is associated with more rapid decline

Long-term effects of medical management on growth and weight in individuals with urea cycle disorders

Low protein diet and sodium or glycerol phenylbutyrate, two pillars of recommended long-term therapy of individuals with urea cycle disorders (UCDs), involve the risk of iatrogenic growth failure. Limited evidence-based studies hamper our knowledge on the long-term effects of the proposed medical management in individuals with UCDs. We studied the impact of medical management on growth and weight development in 307 individuals longitudinally followed by the Urea Cycle Disorders Consortium (UCDC) and the European registry and network for Intoxication type Metabolic Diseases (E-IMD). Intrauterine growth of all investigated UCDs and postnatal linear growth of asymptomatic individuals remained unaffected. Symptomatic individuals were at risk of progressive growth retardation independent from the underlying disease and the degree of natural protein restriction. Growth impairment was determined by disease severity and associated with reduced or borderline plasma branched-chain amino acid (BCAA) concentrations. Liver transplantation appeared to have a beneficial effect on growth. Weight development remained unaffected both in asymptomatic and symptomatic individuals. Progressive growth impairment depends on disease severity and plasma BCAA concentrations, but cannot be predicted by the amount of natural protein intake alone. Future clinical trials are necessary to evaluate whether supplementation with BCAAs might improve growth in UCDs

The V471A polymorphism in autophagy-related gene ATG7 modifies age at onset specifically in Italian Huntington disease patients

The cause of Huntington disease (HD) is a polyglutamine repeat expansion of more than 36 units in the huntingtin protein, which is inversely correlated with the age at onset of the disease. However, additional genetic factors are believed to modify the course and the age at onset of HD. Recently, we identified the V471A polymorphism in the autophagy-related gene ATG7, a key component of the autophagy pathway that plays an important role in HD pathogenesis, to be associated with the age at onset in a large group of European Huntington disease patients. To confirm this association in a second independent patient cohort, we analysed the ATG7 V471A polymorphism in additional 1,464 European HD patients of the “REGISTRY” cohort from the European Huntington Disease Network (EHDN). In the entire REGISTRY cohort we could not confirm a modifying effect of the ATG7 V471A polymorphism. However, analysing a modifying effect of ATG7 in these REGISTRY patients and in patients of our previous HD cohort according to their ethnic origin, we identified a significant effect of the ATG7 V471A polymorphism on the HD age at onset only in the Italian population (327 patients). In these Italian patients, the polymorphism is associated with a 6-years earlier disease onset and thus seems to have an aggravating effect. We could specify the role of ATG7 as a genetic modifier for HD particularly in the Italian population. This result affirms the modifying influence of the autophagic pathway on the course of HD, but also suggests population-specific modifying mechanisms in HD pathogenesis

Identification of genetic variants associated with Huntington's disease progression: a genome-wide association study

Background Huntington's disease is caused by a CAG repeat expansion in the huntingtin gene, HTT. Age at onset has been used as a quantitative phenotype in genetic analysis looking for Huntington's disease modifiers, but is hard to define and not always available. Therefore, we aimed to generate a novel measure of disease progression and to identify genetic markers associated with this progression measure. Methods We generated a progression score on the basis of principal component analysis of prospectively acquired longitudinal changes in motor, cognitive, and imaging measures in the 218 indivduals in the TRACK-HD cohort of Huntington's disease gene mutation carriers (data collected 2008–11). We generated a parallel progression score using data from 1773 previously genotyped participants from the European Huntington's Disease Network REGISTRY study of Huntington's disease mutation carriers (data collected 2003–13). We did a genome-wide association analyses in terms of progression for 216 TRACK-HD participants and 1773 REGISTRY participants, then a meta-analysis of these results was undertaken. Findings Longitudinal motor, cognitive, and imaging scores were correlated with each other in TRACK-HD participants, justifying use of a single, cross-domain measure of disease progression in both studies. The TRACK-HD and REGISTRY progression measures were correlated with each other (r=0·674), and with age at onset (TRACK-HD, r=0·315; REGISTRY, r=0·234). The meta-analysis of progression in TRACK-HD and REGISTRY gave a genome-wide significant signal (p=1·12 × 10−10) on chromosome 5 spanning three genes: MSH3, DHFR, and MTRNR2L2. The genes in this locus were associated with progression in TRACK-HD (MSH3 p=2·94 × 10−8 DHFR p=8·37 × 10−7 MTRNR2L2 p=2·15 × 10−9) and to a lesser extent in REGISTRY (MSH3 p=9·36 × 10−4 DHFR p=8·45 × 10−4 MTRNR2L2 p=1·20 × 10−3). The lead single nucleotide polymorphism (SNP) in TRACK-HD (rs557874766) was genome-wide significant in the meta-analysis (p=1·58 × 10−8), and encodes an aminoacid change (Pro67Ala) in MSH3. In TRACK-HD, each copy of the minor allele at this SNP was associated with a 0·4 units per year (95% CI 0·16–0·66) reduction in the rate of change of the Unified Huntington's Disease Rating Scale (UHDRS) Total Motor Score, and a reduction of 0·12 units per year (95% CI 0·06–0·18) in the rate of change of UHDRS Total Functional Capacity score. These associations remained significant after adjusting for age of onset. Interpretation The multidomain progression measure in TRACK-HD was associated with a functional variant that was genome-wide significant in our meta-analysis. The association in only 216 participants implies that the progression measure is a sensitive reflection of disease burden, that the effect size at this locus is large, or both. Knockout of Msh3 reduces somatic expansion in Huntington's disease mouse models, suggesting this mechanism as an area for future therapeutic investigation