Real Roots of Random Polynomials and Zero Crossing Properties of Diffusion Equation

We study various statistical properties of real roots of three different classes of random polynomials which recently attracted a vivid interest in the context of probability theory and quantum chaos. We first focus on gap probabilities on the real axis, i.e. the probability that these polynomials have no real root in a given interval. For generalized Kac polynomials, indexed by an integer d, of large degree n, one finds that the probability of no real root in the interval [0,1] decays as a power law n^{-\theta(d)} where \theta(d) > 0 is the persistence exponent of the diffusion equation with random initial conditions in spatial dimension d. For n \gg 1 even, the probability that they have no real root on the full real axis decays like n^{-2(\theta(2)+\theta(d))}. For Weyl polynomials and Binomial polynomials, this probability decays respectively like \exp{(-2\theta_{\infty}} \sqrt{n}) and \exp{(-\pi \theta_{\infty} \sqrt{n})} where \theta_{\infty} is such that \theta(d) = 2^{-3/2} \theta_{\infty} \sqrt{d} in large dimension d. We also show that the probability that such polynomials have exactly k roots on a given interval [a,b] has a scaling form given by \exp{(-N_{ab} \tilde \phi(k/N_{ab}))} where N_{ab} is the mean number of real roots in [a,b] and \tilde \phi(x) a universal scaling function. We develop a simple Mean Field (MF) theory reproducing qualitatively these scaling behaviors, and improve systematically this MF approach using the method of persistence with partial survival, which in some cases yields exact results. Finally, we show that the probability density function of the largest absolute value of the real roots has a universal algebraic tail with exponent {-2}. These analytical results are confirmed by detailed numerical computations.Comment: 32 pages, 16 figure

Genetic determinants of telomere length from 109,122 ancestrally diverse whole-genome sequences in TOPMed

Genetic studies on telomere length are important for understanding age-related diseases. Prior GWASs for leukocyte TL have been limited to European and Asian populations. Here, we report the first sequencing-based association study for TL across ancestrally diverse individuals (European, African, Asian, and Hispanic/Latino) from the NHLBI Trans-Omics for Precision Medicine (TOPMed) program. We used whole-genome sequencing (WGS) of whole blood for variant genotype calling and the bioinformatic estimation of telomere length in n = 109,122 individuals. We identified 59 sentinel variants (p < 5 × 10−9) in 36 loci associated with telomere length, including 20 newly associated loci (13 were replicated in external datasets). There was little evidence of effect size heterogeneity across populations. Fine-mapping at OBFC1 indicated that the independent signals colocalized with cell-type-specific eQTLs for OBFC1 (STN1). Using a multi-variant gene-based approach, we identified two genes newly implicated in telomere length, DCLRE1B (SNM1B) and PARN. In PheWAS, we demonstrated that our TL polygenic trait scores (PTSs) were associated with an increased risk of cancer-related phenotypes

Large-scale sequencing identifies multiple genes and rare variants associated with Crohn's disease susceptibility

Genome-wide association studies (GWASs) have identified hundreds of loci associated with Crohn's disease (CD). However, as with all complex diseases, robust identification of the genes dysregulated by noncoding variants typically driving GWAS discoveries has been challenging. Here, to complement GWASs and better define actionable biological targets, we analyzed sequence data from more than 30,000 patients with CD and 80,000 population controls. We directly implicate ten genes in general onset CD for the first time to our knowledge via association to coding variation, four of which lie within established CD GWAS loci. In nine instances, a single coding variant is significantly associated, and in the tenth, ATG4C, we see additionally a significantly increased burden of very rare coding variants in CD cases. In addition to reiterating the central role of innate and adaptive immune cells as well as autophagy in CD pathogenesis, these newly associated genes highlight the emerging role of mesenchymal cells in the development and maintenance of intestinal inflammation.Large-scale sequence-based analyses identify novel risk variants and susceptibility genes for Crohn's disease, and implicate mesenchymal cell-mediated intestinal homeostasis in disease etiology.Cellular mechanisms in basic and clinical gastroenterology and hepatolog

Modulation of the host cell proteome by the intracellular apicomplexan parasite Toxoplasma gondii

To investigate how intracellular parasites manipulate their host cell environment at the molecular level, we undertook a quantitative proteomic study of cells following infection with the apicomplexan parasite Toxoplasma gondii. Using conventional two-dimensional electrophoresis, difference gel electrophoresis (DIGE), and mass spectrometry, we identified host proteins that were consistently modulated in expression following infection. We detected modification of protein expression in key metabolic pathways, including glycolysis, lipid and sterol metabolism, mitosis, apoptosis, and structural-protein expression, suggestive of global reprogramming of cell metabolism by the parasite. Many of the differentially expressed proteins had not been previously implicated in the response to the parasite, while others provide important corroborative protein evidence for previously proposed hypotheses of pathogen-cell interactions. Significantly, over one-third of all modulated proteins were mitochondrial, and this was further investigated by DIGE analysis of a mitochondrion-enriched preparation from infected cells. Comparison of our proteomic data with previous transcriptional studies suggested that a complex relationship exits between transcription and protein expression that may be partly explained by posttranslational modifications of proteins and revealed the importance of investigating protein changes when interpreting transcriptional data. To investigate this further, we used phosphatase treatment and DIGE to demonstrate changes in the phosphorylation states of several key proteins following infection. Overall, our findings indicate that the host cell proteome responds in a dramatic way to T. gondii invasion, in terms of both protein expression changes and protein modifications, and reveal a complex and intimate molecular relationship between host and parasite

Biogenesis of Nanotubular Network in Toxoplasma Parasitophorous Vacuole Induced by Parasite Proteins

The intracellular parasite Toxoplasma gondii develops within a nonfusogenic vacuole containing a network of elongated nanotubules that form connections with the vacuolar membrane. Parasite secretory proteins discharged from dense granules (known as GRA proteins) decorate this intravacuolar network after invasion. Herein, we show using specific gene knockout mutants, that the unique nanotubule conformation of the network is induced by the parasite secretory protein GRA2 and further stabilized by GRA6. The vacuolar compartment generated by GRA2 knockout parasites was dramatically disorganized, and the normally tubular network was replaced by small aggregated material. The defect observed in Δgra2 parasites was evident from the initial stages of network formation when a prominent cluster of multilamellar vesicles forms at a posterior invagination of the parasite. The secretory protein GRA6 failed to localize properly to this posterior organizing center in Δgra2 cells, indicating that this early conformation is essential to proper assembly of the network. Construction of a Δgra6 mutant also led to an altered mature network characterized by small vesicles instead of elongated nanotubules; however, the initial formation of the posterior organizing center was normal. Complementation of the Δgra2 knockout with mutated forms of GRA2 showed that the integrity of both amphipathic alpha-helices of the protein is required for correct formation of the network. The induction of nanotubues by the parasite protein GRA2 may be a conserved feature of amphipathic alpha-helical regions, which have also been implicated in the organization of Golgi nanotubules and endocytic vesicles in mammalian cells

etramps, a New Plasmodium falciparum Gene Family Coding for Developmentally Regulated and Highly Charged Membrane Proteins Located at the Parasite–Host Cell Interface

After invasion of erythrocytes, the human malaria parasite Plasmodium falciparum resides within a parasitophorous vacuole and develops from morphologically and metabolically distinct ring to trophozoite stages. During these developmental phases, major structural changes occur within the erythrocyte, but neither the molecular events governing this development nor the molecular composition of the parasitophorous vacuole membrane (PVM) is well known. Herein, we describe a new family of highly cationic proteins from P. falciparum termed early transcribed membrane proteins (ETRAMPs). Thirteen members were identified sharing a conserved structure, of which six were found only during ring stages as judged from Northern and Western analysis. Other members showed different stage-specific expression patterns. Furthermore, ETRAMPs were associated with the membrane fractions in Western blots, and colocalization and selective permeabilization studies demonstrated that ETRAMPs were located in the PVM. This was confirmed by immunoelectron microscopy where the PVM and tubovesicular extensions of the PVM were labeled. Early expressed ETRAMPs clearly defined separate PVM domains compared with the negatively charged integral PVM protein EXP-1, suggesting functionally different domains in the PVM with an oppositely charged surface coat. We also show that the dynamic change of ETRAMP composition in the PVM coincides with the morphological changes during development. The P. falciparum PVM is an important structure for parasite survival, and its analysis might provide better understanding of the requirements of intracellular parasites