Multigrid reduction-in-time convergence for advection problems: A Fourier analysis perspective

A long-standing issue in the parallel-in-time community is the poor convergence of standard iterative parallel-in-time methods for hyperbolic partial differential equations (PDEs), and for advection-dominated PDEs more broadly. Here, a local Fourier analysis (LFA) convergence theory is derived for the two-level variant of the iterative parallel-in-time method of multigrid reduction-in-time (MGRIT). This closed-form theory allows for new insights into the poor convergence of MGRIT for advection-dominated PDEs when using the standard approach of rediscretizing the fine-grid problem on the coarse grid. Specifically, we show that this poor convergence arises, at least in part, from inadequate coarse-grid correction of certain smooth Fourier modes known as characteristic components, which was previously identified as causing poor convergence of classical spatial multigrid on steady-state advection-dominated PDEs. We apply this convergence theory to show that, for certain semi-Lagrangian discretizations of advection problems, MGRIT convergence using rediscretized coarse-grid operators cannot be robust with respect to CFL number or coarsening factor. A consequence of this analysis is that techniques developed for improving convergence in the spatial multigrid context can be re-purposed in the MGRIT context to develop more robust parallel-in-time solvers. This strategy has been used in recent work to great effect; here, we provide further theoretical evidence supporting the effectiveness of this approach

Chemical Rescue of Active Site Mutants of S. pneumoniae Surface Endonuclease EndA and Other Nucleases of the HNH Family by Imidazole

The His-Asn-His (HNH) motif characterizes the active sites of a large number of different nucleases such as homing endonucleases, restriction endonucleases, structure-specific nucleases and, in particular, nonspecific nucleases. Several biochemical studies have revealed an essential catalytic function for the first amino acid of this motif in HNH nucleases. This histidine residue was identified as the general base that activates a water molecule for a nucleophilic attack on the sugar phosphate backbone of nucleic acids. Replacement of histidine by an amino acid such as glycine or alanine, which lack the catalytically active imidazole side chain, leads to decreases of several orders of magnitude in the nucleolytic activities of members of this nuclease family. We were able, however, to restore the activity of HNH nuclease variants (i.e., EndA (Streptococcus pneumoniae), SmaNuc (Serratia marcescens) and NucA (Anabaena sp.)) that had been inactivated by His→Gly or His→Ala substitution by adding excess imidazole to the inactive enzymes in vitro. Imidazole clearly replaces the missing histidine side chain and thereby restores nucleolytic activity. Significantly, this chemical rescue could also be observed in vivo (Escherichia coli). The in vivo assay might be a promising starting point for the development of a high-throughput screening system for functional EndA inhibitors because, unlike the wild-type enzyme, the H160G and H160A variants of EndA can easily be produced in E. coli. A simple viability assay would allow inhibitors of EndA to be identified because these would counteract the toxicities of the chemically rescued EndA variants. Such inhibitors could be used to block the nucleolytic activity of EndA, which as a surface-exposed enzyme in its natural host destroys the DNA scaffolds of neutrophil extracellular traps (NETs) and thereby allows S. pneumoniae to escape the innate immune response. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Analysis of the mechanism of the Serratia nuclease using site-directed mutagenesis

Based on crystal structure analysis of the Serratia nuclease and a sequence alignment of six related nucleases, conserved amino acid residues that are located in proximity to the previously identified catalytic site residue His89 were selected for a mutagenesis study. Five out of 12 amino acid residues analyzed turned out to be of particular importance for the catalytic activity of the enzyme: Arg57, Arg87, His89, Asn119 and Glu127. Their replacement by alanine, for example, resulted in mutant proteins of very low activity, <1% of the activity of the wild-type enzyme. Steady-state kinetic analysis of the mutant proteins demonstrates that some of these mutants are predominantly affected in their k(cat), others in their K(m). These results and the determination of the pH and metal ion dependence of selected mutant proteins were used for a tentative assignment for the function of these amino acid residues in the mechanism of phosphodiester bond cleavage by the Serratia nuclease

Kinetic analysis of the cleavage of natural and synthetic substrates by the Serratia nuclease

The extracellular nuclease from Serratia marcescens is a non-specific endonuclease that hydrolyzes double-stranded and single-stranded DNA and RNA with high specific activity. Steady-state and pre-steady-state kinetic cleavage experiments were performed with natural and synthetic DNA and RNA substrates to understand the mechanism of action of the Serratia nuclease. Most of the natural substrates are cleaved with similar k(cat) and K(m) values, the k(cat)/K(m) ratios being comparable to that of staphylococcal nuclease. Substrates with extreme structural features, like poly(dA) · poly(dT) or poly(dG) · poly(dC), are cleaved by the Serratia nuclease with a 50 times higher or 10 times lower K(m), respectively, as salmon testis DNA. Neither with natural DNA or RNA nor synthetic oligodeoxynucleotide substrates did we observe substrate inhibition for the Serratia nuclease as reported recently. Experiments with short oligodeoxynucleotides confirmed previous results that for moderately good cleavage activity the substrate should contain at least five phosphate residues. Shorter substrates are still cleaved by the Serratia nuclease, albeit at a rate reduced by a factor of more than 100. Cleavage experiments with oligodeoxynucleotides substituted by a single phosphorothioate group showed that the negative charge of the proR(p)-oxygen of the phosphate group 3' adjacent to the scissile phosphodiester bond is essential for cleavage, as only the R(p)-phosphorothioate supports cleavage at the 5' adjacent phosphodiester bond. Furthermore, the modified bond itself is only cleaved in the R(p)-diastereomer, albeit 1000 times more slowly than the corresponding unmodified phosphodiester bond, which offers the possibility to determine the stereochemical outcome of cleavage. Pre-steady-state cleavage experiments demonstrate that it is not dissociation of products but association of enzyme and substrate or the cleavage of the phosphodiester bond that is the rate-limiting step of the reaction. Finally, it is shown that Serratia nuclease accepts thymidine 3',5'-bis(p-nitrophenyl)phosphate as a substrate and cleaves it at its 5'-end to produce nitrophenol and thymidine 3'-(p-nitrophenylphosphate) 5-phosphate. The rate of cleavage of this artificial substrate, however, is 6-7 orders of magnitude smaller than the rate of cleavage of macromolecular DNA or RNA

The unstructured linker arms of MutL enable GATC site incision beyond roadblocks during initiation of DNA mismatch repair

DNA mismatch repair (MMR) maintains genome stability through repair of DNA replication errors. In Escherichia coli, initiation of MMR involves recognition of the mismatch by MutS, recruitment of MutL, activation of endonuclease MutH and DNA strand incision at a hemimethylated GATC site. Here, we studied the mechanism of communication that couples mismatch recognition to daughter strand incision. We investigated the effect of catalytically-deficient Cas9 as well as stalled RNA polymerase as roadblocks placed on DNA in between the mismatch and GATC site in ensemble and single molecule nanomanipulation incision assays. The MMR proteins were observed to incise GATC sites beyond a roadblock, albeit with reduced efficiency. This residual incision is completely abolished upon shortening the disordered linker regions of MutL. These results indicate that roadblock bypass can be fully attributed to the long, disordered linker regions in MutL and establish that communication during MMR initiation occurs along the DNA backbone

Structure-Based Design of Non-Natural Amino Acid Inhibitors of Amyloid Fibrillation

Many globular and natively disordered proteins can convert into amyloid fibers. These fibers are associated with numerous pathologies1 as well as with normal cellular functions2,3, and frequently form during protein denaturation4,5. Inhibitors of pathological amyloid fibers could serve as leads for therapeutics, provided the inhibitors were specific enough to avoid interfering with normal processes. Here we show that computer-aided, structure-based design can yield highly specific peptide inhibitors of amyloid formation. Using known atomic structures of segments of amyloid fibers as templates, we have designed and characterized an all D-amino acid inhibitor of fibrillation of the tau protein found in Alzheimer’s disease, and a non-natural L-amino acid inhibitor of an amyloid fiber that enhances sexual transmission of HIV. Our results indicate that peptides from structure-based designs can disrupt the fibrillation of full-length proteins, including those like tau that lack fully ordered native structures.We thank M.I. Ivanova, J. Corn, T. Kortemme, D. Anderson, M.R. Sawaya, M. Phillips, S. Sambashivan, J. Park, M. Landau, Q. Zhang, R. Clubb, F. Guo, T. Yeates, J. Nowick, J. Zheng, and M.J. Thompson for discussions, HHMI, NIH, NSF, the GATES foundation, and the Joint Center for Translational Medicine for support, R. Peterson for help with NMR experiments, E. Mandelkow for providing tau constructs, R. Riek for providing amyloid beta, J. Stroud for amyloid beta preparation. Support for JK was from the Damon Runyon Cancer Research Foundation, for HWC by the Ruth L. Kirschstein National Research Service Award, for JM from the programme for junior-professors by the ministry of science, Baden-Württemberg, and for SAS by a UCLA-IGERT bioinformatics traineeship