Combinatorial structure of colored HOMFLY-PT polynomials for torus knots

We rewrite the (extended) Ooguri-Vafa partition function for colored HOMFLY-PT polynomials for torus knots in terms of the free-fermion (semi-infinite wedge) formalism, making it very similar to the generating function for double Hurwitz numbers. This allows us to conjecture the combinatorial meaning of full expansion of the correlation differentials obtained via the topological recursion on the Brini-Eynard-Mari\~no spectral curve for the colored HOMFLY-PT polynomials of torus knots. This correspondence suggests a structural combinatorial result for the extended Ooguri-Vafa partition function. Namely, its coefficients should have a quasi-polynomial behavior, where non-polynomial factors are given by the Jacobi polynomials. We prove this quasi-polynomiality in a purely combinatorial way. In addition to that, we show that the (0,1)- and (0,2)-functions on the corresponding spectral curve are in agreement with the extension of the colored HOMFLY-PT polynomials data.Comment: 40 pages; section 10 addressing the quantum curve was added, as well as some remarks regarding Meixner polynomials thanks to T.Koornwinde

Comparing Three Approaches

Hybridization-based target enrichment protocols require relatively large starting amounts of genomic DNA, which is not always available. Here, we tested three approaches to pre-capture library preparation starting from 10 ng of genomic DNA: (i and ii) whole-genome amplification of DNA samples with REPLI-g (Qiagen) and GenomePlex (Sigma) kits followed by standard library preparation, and (iii) library construction with a low input oriented ThruPLEX kit (Rubicon Genomics). Exome capture with Agilent SureSelectXT2 Human AllExon v4+UTRs capture probes, and HiSeq2000 sequencing were performed for test libraries along with the control library prepared from 1 µg of starting DNA. Tested protocols were characterized in terms of mapping efficiency, enrichment ratio, coverage of the target region, and reliability of SNP genotyping. REPLI-g- and ThruPLEX-FD-based protocols seem to be adequate solutions for exome sequencing of low input sample

Bivariate causal mixture model quantifies polygenic overlap between complex traits beyond genetic correlation.

Accumulating evidence from genome wide association studies (GWAS) suggests an abundance of shared genetic influences among complex human traits and disorders, such as mental disorders. Here we introduce a statistical tool, MiXeR, which quantifies polygenic overlap irrespective of genetic correlation, using GWAS summary statistics. MiXeR results are presented as a Venn diagram of unique and shared polygenic components across traits. At 90% of SNP-heritability explained for each phenotype, MiXeR estimates that 8.3 K variants causally influence schizophrenia and 6.4 K influence bipolar disorder. Among these variants, 6.2 K are shared between the disorders, which have a high genetic correlation. Further, MiXeR uncovers polygenic overlap between schizophrenia and educational attainment. Despite a genetic correlation close to zero, the phenotypes share 8.3 K causal variants, while 2.5 K additional variants influence only educational attainment. By considering the polygenicity, discoverability and heritability of complex phenotypes, MiXeR analysis may improve our understanding of cross-trait genetic architectures

The genetic architecture of the corpus callosum and its subregions

Background: Regional surface area and thickness of the cerebral cortex and volume of subcortical structures are highly heritable brain morphological features with complex genetic architectures, involving many common genetic variants with small effect sizes. However, the genetic architecture of the corpus callosum (CC) and its subregions remains largely unclear. We aim to determine the heritability and genetic architecture of CC volume and each subregion and the extent to which this overlaps with that of psychiatric disorders. Methods: Genetic and T1-weighted MRI data of 40,894 individuals from the UK-biobank was used to construct a multivariate GWAS. Here, we utilized a multivariate approach (Multivariate Omnibus Statistical Test, MOSTest) to assess the distributive effects of common variants across the five subregions of the CC (posterior, mid posterior, central, mid anterior and anterior) obtained by running the automatic subcortical segmentation algorithm in FreeSurfer 5.3. Gene-set enrichment analyses were performed using MAGMA. Linkage disequilibrium score regression was used to determine the SNP-based heritability of the CC and will be used to assess the genetic correlation between each subregion and a variety of psychiatric disorders. Results: Following MOSTest, 70 independent loci show pooled effects across the 5 subregions of the CC (p more than 5×10-8). Using LDSC, we found evidence to suggest that CC volume is heritable (h2SNP= 0.38, SE=0.03). Significant variants showed enrichment in pathways related to regulation of the nervous system and cell development, neurogenesis, and regulation of neuron differentiation. Gene-set analysis revealed 156 significant genes (p is less than 2.6x10-6). Many of the significant SNPs have been previously associated with white matter hyperintensity volume as well as a range of psychiatric disorders. Discussion: Here we provide the first preliminary evidence to suggest that volume of the CC is heritable. Gene set enrichment analyses identified pathways related to neuron development and neurogenesis, suggesting that CC alteration may have an independent developmental origin. Further investigation into the shared genetic architecture of CC subregions and psychiatric disorders may provide novel insight into disease manifestation

Association of Birth Asphyxia With Regional White Matter Abnormalities Among Patients With Schizophrenia and Bipolar Disorders

Importance: White matter (WM) abnormalities are commonly reported in psychiatric disorders. Whether peripartum insufficiencies in brain oxygenation, known as birth asphyxia, are associated with WM of patients with severe mental disorders is unclear. Objective: To examine the association between birth asphyxia and WM in adult patients with schizophrenia and bipolar disorders (BDs) compared with healthy adults. Design, setting, and participants: In this case-control study, all individuals participating in the ongoing Thematically Organized Psychosis project were linked to the Medical Birth Registry of Norway (MBRN), where a subset of 271 patients (case group) and 529 healthy individuals (control group) had undergone diffusion-weighted imaging (DWI). Statistical analyses were performed from June 16, 2020, to March 9, 2021. Exposures: Birth asphyxia was defined based on measures from standardized reporting at birth in the MBRN. Main outcomes and measures: Associations between birth asphyxia and WM regions of interest diffusion metrics, ie, fractional anisotropy (FA), axial diffusivity (AD), and radial diffusivity (RD), were compared between groups using analysis of covariance, adjusted for age, age squared, and sex. Results: Of the 850 adults included in the study, 271 were in the case group (140 [52%] female individuals; mean [SD] age, 28.64 [7.43] years) and 579 were in the control group (245 [42%] female individuals; mean [SD] age, 33.54 [8.31] years). Birth asphyxia measures were identified in 15% to 16% of participants, independent of group. The posterior limb of the internal capsule (PLIC) showed a significant diagnostic group × birth asphyxia interaction (F(1, 843) = 11.46; P = .001), reflecting a stronger association between birth asphyxia and FA in the case group than the control group. RD, but not AD, also displayed a significant diagnostic group × birth asphyxia interaction (F(1, 843) = 9.28; P = .002) in the PLIC, with higher values in patients with birth asphyxia and similar effect sizes as observed for FA. Conclusions and relevance: In this case-control study, abnormalities in the PLIC of adult patients with birth asphyxia may suggest a greater susceptibility to hypoxia in patients with severe mental illness, which could lead to myelin damage or impeded brain development. Echoing recent early-stage schizophrenia studies, abnormalities of the PLIC are relevant to psychiatric disorders, as the PLIC contains important WM brain pathways associated with language, cognitive function, and sensory function, which are impaired in schizophrenia and BDs

Limited association between infections, autoimmune disease and genetic risk and immune activation in severe mental disorders

Background Low-grade inflammation may be part of the underlying mechanism of schizophrenia and bipolar disorder. We investigated if genetic susceptibility, infections or autoimmunity could explain the immune activation. Methods Seven immune markers were selected based on indicated associations to severe mental disorders (IL-1Ra, sIL-2R, IL-18, sgp130, sTNFR-1, APRIL, ICAM-1) and measured in plasma of patients with schizophrenia (SCZ, N = 732) and bipolar spectrum disorders (BD, N = 460) and healthy controls (HC, N = 938). Information on rate of infections and autoimmune diseases were obtained from Norwegian national health registries for a twelve-year period. Polygenic risk scores (PRS) of SCZ and BD were calculated from genome-wide association studies. Analysis of covariance were used to test effects of infection rate, autoimmune disease and PRS on differences in immune markers between patients and HC. Results Infection rate differed between all groups (BD > HC > SCZ, all p < 0.001) whereas autoimmune disease was more frequent in BD compared to SCZ (p = 0.004) and HC (p = 0.003). sIL-2R was positively associated with autoimmune disease (p = 0.001) and negatively associated with PRS of SCZ (p = 0.006) across SCZ and HC; however, associations represented only small changes in the difference of sIL-2R levels between SCZ and HC. Conclusion There were few significant associations between rate of infections, autoimmune disease or PRS and altered immune markers in SCZ and BD, and the detected associations represented only small changes in the immune aberrations. The findings suggest that most of the low-grade inflammation in SCZ and BD is explained by other factors than the underlying PRS, autoimmunity and infection rates.publishedVersio

Shared genetic loci between depression and cardiometabolic traits

Epidemiological and clinical studies have found associations between depression and cardiovascular disease risk factors, and coronary artery disease patients with depression have worse prognosis. The genetic relationship between depression and these cardiovascular phenotypes is not known. We here investigated overlap at the genome-wide level and in individual loci between depression, coronary artery disease and cardiovascular risk factors. We used the bivariate causal mixture model (MiXeR) to quantify genome-wide polygenic overlap and the conditional/conjunctional false discovery rate (pleioFDR) method to identify shared loci, based on genome-wide association study summary statistics on depression (n = 450,619), coronary artery disease (n = 502,713) and nine cardiovascular risk factors (n = 204,402–776,078). Genetic loci were functionally annotated using FUnctional Mapping and Annotation (FUMA). Of 13.9K variants influencing depression, 9.5K (SD 1.0K) were shared with body-mass index. Of 4.4K variants influencing systolic blood pressure, 2K were shared with depression. ConjFDR identified 79 unique loci associated with depression and coronary artery disease or cardiovascular risk factors. Six genomic loci were associated jointly with depression and coronary artery disease, 69 with blood pressure, 49 with lipids, 9 with type 2 diabetes and 8 with c-reactive protein at conjFDR < 0.05. Loci associated with increased risk for depression were also associated with increased risk of coronary artery disease and higher total cholesterol, low-density lipoprotein and c-reactive protein levels, while there was a mixed pattern of effect direction for the other risk factors. Functional analyses of the shared loci implicated metabolism of alpha-linolenic acid pathway for type 2 diabetes. Our results showed polygenic overlap between depression, coronary artery disease and several cardiovascular risk factors and suggest molecular mechanisms underlying the association between depression and increased cardiovascular disease risk.publishedVersio

Characterizing the Genetic Overlap Between Psychiatric Disorders and Sleep-Related Phenotypes

Background: A range of sleep disturbances are commonly experienced by patients with psychiatric disorders, and genome-wide genetic analyses have shown some significant genetic correlations between these traits. Here, we applied novel statistical genetic methodologies to better characterize the potential shared genetic architecture between sleep-related phenotypes and psychiatric disorders. Methods: Using the MiXeR method, which can estimate polygenic overlap beyond genetic correlation, the shared genetic architecture between major psychiatric disorders (bipolar disorder [N = 51,710], depression [N = 480,359], and schizophrenia [N = 77,096]) and sleep-related phenotypes (chronotype [N = 449,734], insomnia [N = 386,533] and sleep duration [N = 446,118]) were quantified on the basis of genetic summary statistics. Furthermore, the conditional/conjunctional false discovery rate framework was used to identify specific shared loci between these phenotypes, for which positional and functional annotation were conducted with FUMA. Results: Extensive genetic overlap between the sleep-related phenotypes and bipolar disorder (63%–77%), depression (76%–79%), and schizophrenia (64%–79%) was identified, with moderate levels of congruence between most investigated traits (47%–58%). Specific shared loci were identified for all bivariate analyses, and a subset of 70 credible genes were mapped to these shared loci. Conclusions: The current results provide evidence for substantial polygenic overlap between psychiatric disorders and sleep-related phenotypes, beyond genetic correlation (|rg| = 0.02 to 0.42). Moderate congruency within the shared genetic components suggests a complex genetic relationship and potential subgroups with higher or lower genetic concordance. This work provides new insights and understanding of the shared genetic etiology of sleep-related phenotypes and psychiatric disorders and highlights new opportunities and avenues for future investigation.publishedVersio