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

Replication of MHV_H277A in primary macrophages with deficiencies in the IFN-I induction pathway.

<p>Kinetics of viral replication (left panels) and IFN-β mRNA (right panels) in bone marrow-derived macrophages deficient for Mda5 <b>(a)</b>, MAVS <b>(b)</b> and in macrophages triple knockout for IRF3, IRF5 and IRF7 <b>(c)</b> following infection with MHV-A59 and MHV_H277A (MOI = 1). (<b>d</b>) IFN-β in the supernatant of infected macrophages was measured using an ELISA. All values were outside of the detection limit of 15.6 pg/ml (dashed line) and thus depicted as ND (not detected). (<b>a-d</b>) Data represent three independent experiments, each performed in two to three replicas. <b>(a)</b> The difference in peak levels of viral titers (MHV-A59: 4.9, MHV_H277A: 3.0) was statistically significant (p<0.001), the difference in peak levels of IFN-β expression (MHV-A59: 9.2, MHV_H277A: 7.8) was statistically not significant (p = 0.44). <b>(b)</b> The differences in peak levels of viral titers (MHV-A59: 5.5, MHV_H277A: 3.9) and IFN-β expression (MHV-A59: 9.1, MHV_H277A: 12.1) were statistically significant (p<0.001, p = 0.024, respectively). <b>(c)</b> The difference in peak levels of viral titers (MHV-A59: 5.5, MHV_H277A: 4.9) was statistically significant (p = 0.002). The difference in peak levels of IFN-β expression (MHV-A59: 6.5, MHV_H277A: 5.1) was statistically not significant (p = 0.368). Mean and SEM are depicted. The 95% confidence band is highlighted in grey. Statistically significant comparisons are displayed; * p < 0.05, ** < 0.01, *** < 0.001.</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

EndoU-deficient MHV induces activation of the OAS-RNase L pathway, resulting in early breakdown of ribosomal RNA.

<p>(<b>a</b>) Analysis of rRNA integrity in bone marrow-derived macrophages derived from wild type C57BL/6, Mda5^-/-, RNase L^-/-, and IFNAR^-/- mice following infection with MHV-A59 and MHV_H277A (MOI = 1). Total RNA was isolated at indicated time points and degradation of ribosomal RNA as marker for RNase L activation was assessed with a Fragment Analyzer. One representative picture and migration of 18S and 28S ribosomal RNA is displayed. The RNA Quality Number (RQN) is indicated. (<b>b</b>) The integrity of rRNA from MHV-A59 and MHV_H277A infected (MOI = 1) L929 cells, with or without IFN-I pre-treatment (12.5 U of IFN-I 16h prior to infection). Analysis was performed as in panel (<b>a</b>) and one representative image out of five is displayed.</p