Asymptotic Expansions for Sub-Critical Lagrangean Forms

Asymptotic expansions for the Taylor coefficients of the Lagrangean form phi(z)=zf(phi(z)) are examined with a focus on the calculations of the asymptotic coefficients. The expansions are simple and useful, and we discuss their use in some enumerating sequences in trees, lattice paths and planar maps

Early endonuclease-mediated evasion of RNA sensing ensures efficient coronavirus replication.

Coronaviruses are of veterinary and medical importance and include highly pathogenic zoonotic viruses, such as SARS-CoV and MERS-CoV. They are known to efficiently evade early innate immune responses, manifesting in almost negligible expression of type-I interferons (IFN-I). This evasion strategy suggests an evolutionary conserved viral function that has evolved to prevent RNA-based sensing of infection in vertebrate hosts. Here we show that the coronavirus endonuclease (EndoU) activity is key to prevent early induction of double-stranded RNA (dsRNA) host cell responses. Replication of EndoU-deficient coronaviruses is greatly attenuated in vivo and severely restricted in primary cells even during the early phase of the infection. In macrophages we found immediate induction of IFN-I expression and RNase L-mediated breakdown of ribosomal RNA. Accordingly, EndoU-deficient viruses can retain replication only in cells that are deficient in IFN-I expression or sensing, and in cells lacking both RNase L and PKR. Collectively our results demonstrate that the coronavirus EndoU efficiently prevents simultaneous activation of host cell dsRNA sensors, such as Mda5, OAS and PKR. The localization of the EndoU activity at the site of viral RNA synthesis-within the replicase complex-suggests that coronaviruses have evolved a viral RNA decay pathway to evade early innate and intrinsic antiviral host cell responses

Phase transitions from exp⁡(n1/2)\exp(n^{1/2}) to exp⁡(n2/3)\exp(n^{2/3}) in the asymptotics of banded plane partitions

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Replication of EndoU-deficient MHV is partially restored in IFNAR^-/- macrophages and EndoU mutants display a pronounced sensitivity to IFN-I treatment.

<p>(<b>a</b>) Replication kinetics of MHV-A59 and MHV_H277A (left panel; titers in pfu) and cell-associated viral RNA (right panel; qRT-PCR) following infection of IFNAR^-/- bone marrow-derived macrophages (MOI = 1). Data represent four independent experiments, each performed in two to three replicas. Mean and SEM are depicted. The 95% confidence band is highlighted in grey. The differences in peak levels of viral titers (MHV-A59: 6.0, MHV_H277A: 5.2) and RNA copies (MHV-A59: 9.7, MHV_H277A: 9.3) were statistically significant (p<0.001, p = 0.032, respectively). (<b>b</b>) Expression of IFN-β mRNA (left panel; qRT-PCR) and protein (right panel; ELISA) in IFNAR^-/- macrophages following infection of MHV-A59 and MHV_H277A (MOI = 1). Data represent four (left panel) and three (right panel) independent experiments, each performed in two to three replicas. Median and the 1–99 percentiles are displayed. Dashed line depicts limit of detection (right panel). The difference in peak levels of IFN-β expression (MHV-A59: 9.4, MHV_H277A: 13.8) was statistically significant (p = 0.002). Significance of IFN-β expression was assesses by a Wilcoxon matched-pairs test, * p < 0.05. ND, not detected. (<b>c</b>) Sensitivity of wild type and EndoU-deficient MHV (left panel) and HCoV-229E (right panel) viruses to IFN-I pre-treatment (4 h) in L929 cells (left panel) and MRC-5 cells (right panel) with various dosages of IFN-I (MOI = 1). Virus replication was measured at 24 h.p.i. by plaque assay (MHV) and at 48 h.p.i. by qRT-PCR (HCoV-229E), respectively. Data represent three independent experiments, each performed in two to three replicas. Data are displayed as differences to untreated controls and statistical comparisons between wild type and EndoU-deficient viruses were performed for each concentration. Mean and SEM are displayed. Data points that show significant differences in a two-sided, unpaired Student’s t-test are depicted. * p < 0.05, ** p < 0.01 and *** p < 0001.</p

The CoV endoribonuclease is essential for replication and spread in vivo.

<p>(<b>a</b>) Genome organization of the EndoU-deficient murine hepatitis virus (MHV) with an active site His to Ala substitution (MHV_H277A) and a corresponding human coronavirus 229E mutant (HCoV-229E_H250A) in the non-structural protein 15. (<b>b</b>) Replication kinetics of MHV-A59 and MHV_H277A in murine L929 fibroblasts after infection at a MOI of 1 and 0.1, presented as viral titer in plaque forming units (pfu). Data represent two independent experiments, each performed in duplicates. Mean and SEM are depicted. The 95% confidence band is highlighted in grey. The differences in peak levels of viral titers were calculated by using the non-linear regression model described in Material and Methods (peak MHV-A59: 6.0, MHV_H277A: 5.6, p = 0.024, left panel; peak MHV-A59: 6.6, MHV_H277A: 6.0, p = 0.016, right panel) and significance is displayed as * p < 0.05. (<b>c</b>) Viral titers of MHV-A59 and MHV_H277A in liver and spleen of C57BL/6, IFNAR^-/-, Mda5^-/-, TLR7^-/-, and Mda5^-/-/TLR7^-/- mice at two days post intraperitoneal infection (500 pfu). Data represent three to four independent experiments, each based on two to three mice per strain and virus. Mean and SEM are depicted. Data points that show significant differences in a two-sided, unpaired Student’s t-test are displayed; * p < 0.05, ** < 0.01, *** < 0.001. ND, not detected.</p

Infection with EndoU-deficient MHV results in increased cytosolic dsRNA.

<p><b>(a-b)</b> Intracellular staining of dsRNA and FACS analysis of MHV-A59 and MHV_H277A infected (MOI = 1) C57BL/6 <b>(a)</b> and IFNAR^-/- <b>(b)</b> macrophages at 4, 6, 9 and 12 h.p.i.. One representative histogram out of two (a) and three (b) is shown for each time point. Cells without virus infection (mock) were used as controls. <b>(c-d)</b> The left panels show cells that were co-stained for MHV-nsp2/3 to control for MHV-A59 and MHV_H277A infection. The right panels display the median fluorescent intensity (MFI) of dsRNA peaks detected in <b>(a-b).</b> The left panels show data from two (c) and three (d) independent experiments. Cells without virus infection (mock) were used as controls. Mean and SEM are depicted. The 95% confidence band is highlighted in grey. Statistically significant comparisons are displayed (**, p< 0.01).</p