An Entropy Stable Nodal Discontinuous Galerkin Method for the Two Dimensional Shallow Water Equations on Unstructured Curvilinear Meshes with Discontinuous Bathymetry

We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the nonlinear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretisation exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretisation of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem

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Signal recognition particle prevents N-terminal processing of bacterial membrane proteins.

Bacterial proteins are synthesized with an N-formylated amino-terminal methionine, and N-formylated peptides elicit innate-immunity responses against bacterial infections. However, the source of these formylated peptides is not clear, as most bacterial proteins are co-translationally deformylated by peptide deformylase. Here we develop a deformylation assay with translating ribosomes as substrates, to show that the binding of the signal recognition particle (SRP) to signal sequences in nascent proteins on the ribosome prevents deformylation, whereas deformylation of nascent proteins without signal sequence is not affected. Deformylation and its inhibition by SRP are not influenced by trigger factor, a chaperone that interacts with nascent chains on the ribosome. We propose that bacterial inner-membrane proteins, in particular those with N-out topology, can retain their N-terminal formyl group during cotranslational membrane insertion and supply formylated peptides during bacterial infections

Conformational changes of the small ribosomal subunit during elongation factor G-dependent tRNA–mRNA translocation.

Translocation, a coordinated movement of two tRNAs together with mRNA on the ribosome, is catalyzed by elongation factor G (EF-G). The reaction is accompanied by conformational rearrangements of the ribosome that are, as yet, not well characterized. Here, we analyze those rearrangements by restricting the conformational flexibility of the ribosome by antibiotics binding to specific sites of the ribosome. Paromomycin (Par), viomycin (Vio), spectinomycin (Spc), and hygromycin B (HygB) inhibited the tRNA-mRNA movement, while the other partial reactions of translocation, including the unlocking rearrangement of the ribosome that precedes tRNA-mRNA movement, were not affected. The functional cycle of EF-G, i.e. binding of EF-G(.)GTP to the ribosome, GTP hydrolysis, Pi release, and dissociation of EF-G(.)GDP from the ribosome, was not affected either, indicating that EF-G turnover is not coupled directly to tRNA-mRNA movement. The inhibition of translocation. by Par and Vio is attributed to the stabilization of tRNA binding in the A site, whereas Spc and HygB had a direct inhibitory effect on tRNA-mRNA movement. Streptomycin (Str) had essentially no effect on translocation, although it caused a large increase in tRNA affinity to the A site. These results suggest that conformational changes in the vicinity of the decoding region at the binding sites of Spc and HygB are important for tRNA-mRNA movement, whereas Str seems to stabilize a conformation of the ribosome that is prone to rapid translocation, thereby compensating the effect on tRNA affinity. (C) 2004 Elsevier Ltd. All rights reserved

Control of phosphate release from elongation factor G by ribosomal protein L7/12.

Ribosomal protein L7/12 is crucial for the function of elongation factor G (EF-G) on the ribosome. Here, we report the localization of a site in the C-terminal domain (CTD) of L7/12 that is critical for the interaction with EF-G. Single conserved surface amino acids were replaced in the CTD of L7/12. Whereas mutations in helices 5 and 6 had no effect, replacements of V66, I69, K70, and R73 in helix 4 increased the Michaelis constant (K(M)) of EF-G·GTP for the ribosome, suggesting an involvement of these residues in EF-G binding. The mutations did not appreciably affect rapid single-round GTP hydrolysis and had no effect on tRNA translocation on the ribosome. In contrast, the release of inorganic phosphate (Pi) from ribosome-bound EF-G·GDP·Pi was strongly inhibited and became rate-limiting for the turnover of EF-G. The control of Pi release by interactions between EF-G and L7/12 appears to be important for maintaining the conformational coupling between EF-G and the ribosome for translocation and for timing the dissociation of the factor from the ribosome

Involvement of helix 34 of 16 S rRNA in decoding and translocation on the ribosome.

Helix 34 of 16 S rRNA is located in the head of the 30 S ribosomal subunit close to the decoding center and has been invoked in a number of ribosome functions. In the present work, we have studied the effects of mutations in helix 34 both in vivo and in vitro. Several nucleotides in helix 34 that are either highly conserved or form important tertiary contacts in 16 S rRNA (U961, C1109, A1191, and A1201) were mutated, and the mutant ribosomes were expressed in the Escherichia coli MC250 Delta 7 strain that lacks all seven chromosomal rRNA operons. Mutations at positions A1191 and U961 reduced the efficiency of subunit association and resulted in structural rearrangements in helix 27 (position 908) and helix 31 (position 974) of 16 S rRNA. All mutants exhibited increased levels of frameshifting and nonsense readthrough. The effects on frameshifting were specific in that-1 frameshifting was enhanced with mutant A1191G and-1 frameshifting with the other mutants. Mutations of A1191 moderately (similar to 2-fold) inhibited tRNA translocation. No significant effects were found on efficiency and rate of initiation, misreading of sense codons, or binding of tRNA to the E site. The data indicate that helix 34 is involved in controlling the maintenance of the reading frame and in tRNA translocation

Conformationally restricted elongation factor G retains GTPase activity but is inactive in translocation on the ribosome.

Elongation factor G (EF-G) from Escherichia coli is a large, five-domain GTPase that promotes tRNA translocation on the ribosome. Full activity requires GTP hydrolysis, suggesting that a conformational change of the factor is important for function. To restrict the intramolecular mobility, two cysteine residues were engineered into domains 1 and 5 of EF-G that spontaneously formed a disulfide cross-link. Cross-linked EF-G retained GTPase activity on the ribosome, whereas it was inactive in translocation as well as in turnover. Both activities were restored when the cross-link was reversed by reduction. These results strongly argue against a GTPase switch-type model of EF-G function and demonstrate that conformational mobility is an absolute requirement for EF-G function on the ribosome