Continuous, Semi-discrete, and Fully Discretized Navier-Stokes Equations

The Navier--Stokes equations are commonly used to model and to simulate flow phenomena. We introduce the basic equations and discuss the standard methods for the spatial and temporal discretization. We analyse the semi-discrete equations -- a semi-explicit nonlinear DAE -- in terms of the strangeness index and quantify the numerical difficulties in the fully discrete schemes, that are induced by the strangeness of the system. By analyzing the Kronecker index of the difference-algebraic equations, that represent commonly and successfully used time stepping schemes for the Navier--Stokes equations, we show that those time-integration schemes factually remove the strangeness. The theoretical considerations are backed and illustrated by numerical examples.Comment: 28 pages, 2 figure, code available under DOI: 10.5281/zenodo.998909, https://doi.org/10.5281/zenodo.99890

Analysis of natural variants of the hepatitis C virus internal ribosome entry site reveals that primary sequence plays a key role in cap-independent translation

The HCV internal ribosome entry site (IRES) spans a region of ∼340 nt that encompasses most of the 5′ untranslated region (5′UTR) of the viral mRNA and the first 24–40 nt of the core-coding region. To investigate the implication of altering the primary sequence of the 5′UTR on IRES activity, naturally occurring variants of the 5′UTR were isolated from clinical samples and analyzed. The impact of the identified mutations on translation was evaluated in the context of RLuc/FLuc bicistronic RNAs. Results show that depending on their location within the RNA structure, these naturally occurring mutations cause a range of effects on IRES activity. However, mutations within subdomain IIId hinder HCV IRES-mediated translation. In an attempt to explain these data, the dynamic behavior of the subdomain IIId was analyzed by means of molecular dynamics (MD) simulations. Despite the loss of function, MD simulations predicted that mutant G266A/G268U possesses a structure similar to the wt-RNA. This prediction was validated by analyzing the secondary structure of the isolated IIId RNAs by circular dichroism spectroscopy in the presence or absence of Mg2+ ions. These data strongly suggest that the primary sequence of subdomain IIId plays a key role in HCV IRES-mediated translation

Thriving under Stress: Selective Translation of HIV-1 Structural Protein mRNA during Vpr-Mediated Impairment of eIF4E Translation Activity

Translation is a regulated process and is pivotal to proper cell growth and homeostasis. All retroviruses rely on the host translational machinery for viral protein synthesis and thus may be susceptible to its perturbation in response to stress, co-infection, and/or cell cycle arrest. HIV-1 infection arrests the cell cycle in the G2/M phase, potentially disrupting the regulation of host cell translation. In this study, we present evidence that HIV-1 infection downregulates translation in lymphocytes, attributable to the cell cycle arrest induced by the HIV-1 accessory protein Vpr. The molecular basis of the translation suppression is reduced accumulation of the active form of the translation initiation factor 4E (eIF4E). However, synthesis of viral structural proteins is sustained despite the general suppression of protein production. HIV-1 mRNA translation is sustained due to the distinct composition of the HIV-1 ribonucleoprotein complexes. RNA-coimmunoprecipitation assays determined that the HIV-1 unspliced and singly spliced transcripts are predominantly associated with nuclear cap binding protein 80 (CBP80) in contrast to completely-spliced viral and cellular mRNAs that are associated with eIF4E. The active translation of the nuclear cap binding complex (CBC)-bound viral mRNAs is demonstrated by ribosomal RNA profile analyses. Thus, our findings have uncovered that the maintenance of CBC association is a novel mechanism used by HIV-1 to bypass downregulation of eIF4E activity and sustain viral protein synthesis. We speculate that a subset of CBP80-bound cellular mRNAs contribute to recovery from significant cellular stress, including human retrovirus infection

General RNA-binding proteins have a function in poly(A)-binding protein-dependent translation

The interaction between the poly(A)-binding protein (PABP) and eukaryotic translational initiation factor 4G (eIF4G), which brings about circularization of the mRNA, stimulates translation. General RNA-binding proteins affect translation, but their role in mRNA circularization has not been studied before. Here, we demonstrate that the major mRNA ribonucleoprotein YB-1 has a pivotal function in the regulation of eIF4F activity by PABP. In cell extracts, the addition of YB-1 exacerbated the inhibition of 80S ribosome initiation complex formation by PABP depletion. Rabbit reticulocyte lysate in which PABP weakly stimulates translation is rendered PABP-dependent after the addition of YB-1. In this system, eIF4E binding to the cap structure is inhibited by YB-1 and stimulated by a nonspecific RNA. Significantly, adding PABP back to the depleted lysate stimulated eIF4E binding to the cap structure more potently if this binding had been downregulated by YB-1. Conversely, adding nonspecific RNA abrogated PABP stimulation of eIF4E binding. These data strongly suggest that competition between YB-1 and eIF4G for mRNA binding is required for efficient stimulation of eIF4F activity by PABP