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Abstract We discuss random interpolating sequences in weighted Dirichlet spaces $${{\mathcal{D}}}_\alpha $$, $$0\leq \alpha \leq 1$$, when the radii of the sequence points are fixed a priori and the arguments are uniformly distributed. Although conditions for deterministic interpolation in these spaces depend on capacities, which are very hard to estimate in general, we show that random interpolation is driven by surprisingly simple distribution conditions. As a consequence, we obtain a breakpoint at $$\alpha =1/2$$ in the behavior of these random interpolating sequences showing more precisely that almost sure interpolating sequences for $${{\mathcal{D}}}_\alpha $$ are exactly the almost sure separated sequences when $$0\le \alpha <1/2$$ (which includes the Hardy space $$H^2={{\mathcal{D}}}_0$$), and they are exactly the almost sure zero sequences for $${{\mathcal{D}}}_\alpha $$ when $$1/2 \leq \alpha \le 1$$ (which includes the classical Dirichlet space $${{\mathcal{D}}}={{\mathcal{D}}}_1$$). 

Abstract Single-molecule Förster-resonance energy transfer (smFRET) experiments allow the study of biomolecular structure and dynamics in vitro and in vivo. We performed an international blind study involving 19 laboratories to assess the uncertainty of FRET experiments for proteins with respect to the measured FRET efficiency histograms, determination of distances, and the detection and quantification of structural dynamics. Using two protein systems with distinct conformational changes and dynamics, we obtained an uncertainty of the FRET efficiency ≤0.06, corresponding to an interdye distance precision of ≤2 Å and accuracy of ≤5 Å. We further discuss the limits for detecting fluctuations in this distance range and how to identify dye perturbations. Our work demonstrates the ability of smFRET experiments to simultaneously measure distances and avoid the averaging of conformational dynamics for realistic protein systems, highlighting its importance in the expanding toolbox of integrative structural biology. 

Tourette syndrome (TS) is characterized by multiple motor and vocal tics, and high-comorbidity rates with other neuropsychiatric disorders. Obsessive compulsive disorder (OCD), attention deficit hyperactivity disorder (ADHD), autism spectrum disorders (ASDs), major depressive disorder (MDD), and anxiety disorders (AXDs) are among the most prevalent TS comorbidities. To date, studies on TS brain structure and function have been limited in size with efforts mostly fragmented. This leads to low-statistical power, discordant results due to differences in approaches, and hinders the ability to stratify patients according to clinical parameters and investigate comorbidity patterns. Here, we present the scientific premise, perspectives, and key goals that have motivated the establishment of the Enhancing Neuroimaging Genetics through Meta-Analysis for TS (ENIGMA-TS) working group. The ENIGMA-TS working group is an international collaborative effort bringing together a large network of investigators who aim to understand brain structure and function in TS and dissect the underlying neurobiology that leads to observed comorbidity patterns and clinical heterogeneity. Previously collected TS neuroimaging data will be analyzed jointly and integrated with TS genomic data, as well as equivalently large and already existing studies of highly comorbid OCD, ADHD, ASD, MDD, and AXD. Our work highlights the power of collaborative efforts and transdiagnostic approaches, and points to the existence of different TS subtypes. ENIGMA-TS will offer large-scale, high-powered studies that will lead to important insights toward understanding brain structure and function and genetic effects in TS and related disorders, and the identification of biomarkers that could help inform improved clinical practice. 

Abstract Tourette syndrome (TS) is a neuropsychiatric disorder of complex genetic architecture involving multiple interacting genes. Here, we sought to elucidate the pathways that underlie the neurobiology of the disorder through genome-wide analysis. We analyzed genome-wide genotypic data of 3581 individuals with TS and 7682 ancestry-matched controls and investigated associations of TS with sets of genes that are expressed in particular cell types and operate in specific neuronal and glial functions. We employed a self-contained, set-based association method (SBA) as well as a competitive gene set method (MAGMA) using individual-level genotype data to perform a comprehensive investigation of the biological background of TS. Our SBA analysis identified three significant gene sets after Bonferroni correction, implicating ligand-gated ion channel signaling, lymphocytic, and cell adhesion and transsynaptic signaling processes. MAGMA analysis further supported the involvement of the cell adhesion and trans-synaptic signaling gene set. The lymphocytic gene set was driven by variants in FLT3 , raising an intriguing hypothesis for the involvement of a neuroinflammatory element in TS pathogenesis. The indications of involvement of ligand-gated ion channel signaling reinforce the role of GABA in TS, while the association of cell adhesion and trans-synaptic signaling gene set provides additional support for the role of adhesion molecules in neuropsychiatric disorders. This study reinforces previous findings but also provides new insights into the neurobiology of TS. 

Abstract Tourette Syndrome (TS) is a complex neurodevelopmental disorder characterized by vocal and motor tics lasting more than a year. It is highly polygenic in nature with both rare and common previously associated variants. Epidemiological studies have shown TS to be correlated with other phenotypes, but large-scale phenome wide analyses in biobank level data have not been performed to date. In this study, we used the summary statistics from the latest meta-analysis of TS to calculate the polygenic risk score (PRS) of individuals in the UK Biobank data and applied a Phenome Wide Association Study (PheWAS) approach to determine the association of disease risk with a wide range of phenotypes. A total of 57 traits were found to be significantly associated with TS polygenic risk, including multiple psychosocial factors and mental health conditions such as anxiety disorder and depression. Additional associations were observed with complex non-psychiatric disorders such as Type 2 diabetes, heart palpitations, and respiratory conditions. Cross-disorder comparisons of phenotypic associations with genetic risk for other childhood-onset disorders (e.g.: attention deficit hyperactivity disorder [ADHD], autism spectrum disorder [ASD], and obsessive-compulsive disorder [OCD]) indicated an overlap in associations between TS and these disorders. ADHD and ASD had a similar direction of effect with TS while OCD had an opposite direction of effect for all traits except mental health factors. Sex-specific PheWAS analysis identified differences in the associations with TS genetic risk between males and females. Type 2 diabetes and heart palpitations were significantly associated with TS risk in males but not in females, whereas diseases of the respiratory system were associated with TS risk in females but not in males. This analysis provides further evidence of shared genetic and phenotypic architecture of different complex disorders.