BoMb-OT: On Batch of Mini-batches Optimal Transport

Mini-batch optimal transport (m-OT) has been successfully used in practical applications that involve probability measures with intractable density, or probability measures with a very high number of supports. The m-OT solves several sparser optimal transport problems and then returns the average of their costs and transportation plans. Despite its scalability advantage, the m-OT does not consider the relationship between mini-batches which leads to undesirable estimation. Moreover, the m-OT does not approximate a proper metric between probability measures since the identity property is not satisfied. To address these problems, we propose a novel mini-batching scheme for optimal transport, named Batch of Mini-batches Optimal Transport (BoMb-OT), that finds the optimal coupling between mini-batches and it can be seen as an approximation to a well-defined distance on the space of probability measures. Furthermore, we show that the m-OT is a limit of the entropic regularized version of the BoMb-OT when the regularized parameter goes to infinity. Finally, we carry out extensive experiments to show that the BoMb-OT can estimate a better transportation plan between two original measures than the m-OT. It leads to a favorable performance of the BoMb-OT in the matching and color transfer tasks. Furthermore, we observe that the BoMb-OT also provides a better objective loss than the m-OT for doing approximate Bayesian computation, estimating parameters of interest in parametric generative models, and learning non-parametric generative models with gradient flow.Comment: 36 pages, 20 figure

A Widespread Bacterial Type VI Secretion Effector Superfamily Identified Using a Heuristic Approach

SummarySophisticated mechanisms are employed to facilitate information exchange between interfacing bacteria. A type VI secretion system (T6SS) of Pseudomonas aeruginosa was shown to deliver cell wall-targeting effectors to neighboring cells. However, the generality of bacteriolytic effectors and, moreover, of antibacterial T6S remained unknown. Using parameters derived from experimentally validated bacterial T6SS effectors we identified a phylogenetically disperse superfamily of T6SS-associated peptidoglycan-degrading effectors. The effectors separate into four families composed of peptidoglycan amidase enzymes of differing specificities. Effectors strictly co-occur with cognate immunity proteins, indicating that self-intoxication is a general property of antibacterial T6SSs and effector delivery by the system exerts a strong selective pressure in nature. The presence of antibacterial effectors in a plethora of organisms, including many that inhabit or infect polymicrobial niches in the human body, suggests that the system could mediate interbacterial interactions of both environmental and clinical significance

Structural basis for type VI secreted peptidoglycan DL-endopeptidase function, specificity and neutralization in <em>Serratia marcescens</em>

Some Gram-negative bacteria target their competitors by exploiting the type VI secretion system to extrude toxic effector proteins. To prevent self-harm, these bacteria also produce highly specific immunity proteins that neutralize these antagonistic effectors. Here, the peptidoglycan endopeptidase specificity of two type VI secretion-system-associated effectors from Serratia marcescens is characterized. These small secreted proteins, Ssp1 and Ssp2, cleave between γ-d-glutamic acid and l-meso-diaminopimelic acid with different specificities. Ssp2 degrades the acceptor part of cross-linked tetratetrapeptides. Ssp1 displays greater promiscuity and cleaves monomeric tripeptides, tetrapeptides and pentapeptides and dimeric tetratetra and tetrapenta muropeptides on both the acceptor and donor strands. Functional assays confirm the identity of a catalytic cysteine in these endopeptidases and crystal structures provide information on the structure–activity relationships of Ssp1 and, by comparison, of related effectors. Functional assays also reveal that neutralization of these effectors by their cognate immunity proteins, which are called resistance-associated proteins (Raps), contributes an essential role to cell fitness. The structures of two immunity proteins, Rap1a and Rap2a, responsible for the neutralization of Ssp1 and Ssp2-like endopeptidases, respectively, revealed two distinct folds, with that of Rap1a not having previously been observed. The structure of the Ssp1–Rap1a complex revealed a tightly bound heteromeric assembly with two effector molecules flanking a Rap1a dimer. A highly effective steric block of the Ssp1 active site forms the basis of effector neutralization. Comparisons with Ssp2–Rap2a orthologues suggest that the specificity of these immunity proteins for neutralizing effectors is fold-dependent and that in cases where the fold is conserved sequence differences contribute to the specificity of effector–immunity protein interactions

A widespread family of bacterial cell wall assembly proteins

Teichoic acids and acidic capsular polysaccharides are major anionic cell wall polymers (APs) in many bacteria, with various critical cell functions, including maintenance of cell shape and structural integrity, charge and cation homeostasis, and multiple aspects of pathogenesis. We have identified the widespread LytR–Cps2A–Psr (LCP) protein family, of previously unknown function, as novel enzymes required for AP synthesis. Structural and biochemical analysis of several LCP proteins suggest that they carry out the final step of transferring APs from their lipid-linked precursor to cell wall peptidoglycan (PG). In Bacillus subtilis, LCP proteins are found in association with the MreB cytoskeleton, suggesting that MreB proteins coordinate the insertion of the major polymers, PG and AP, into the cell wall

Specialized Peptidoglycan Hydrolases Sculpt the Intra-bacterial Niche of Predatory Bdellovibrio and Increase Population Fitness

Bdellovibrio are predatory bacteria that have evolved to invade virtually all Gram-negative bacteria, including many prominent pathogens. Upon invasion, prey bacteria become rounded up into an osmotically stable niche for the Bdellovibrio, preventing further superinfection and allowing Bdellovibrio to replicate inside without competition, killing the prey bacterium and degrading its contents. Historically, prey rounding was hypothesized to be associated with peptidoglycan (PG) metabolism; we found two Bdellovibrio genes, bd0816 and bd3459, expressed at prey entry and encoding proteins with limited homologies to conventional dacB/PBP4 DD-endo/carboxypeptidases (responsible for peptidoglycan maintenance during growth and division). We tested possible links between Bd0816/3459 activity and predation. Bd3459, but not an active site serine mutant protein, bound β-lactam, exhibited DD-endo/carboxypeptidase activity against purified peptidoglycan and, importantly, rounded up E. coli cells upon periplasmic expression. A ΔBd0816 ΔBd3459 double mutant invaded prey more slowly than the wild type (with negligible prey cell rounding) and double invasions of single prey by more than one Bdellovibrio became more frequent. We solved the crystal structure of Bd3459 to 1.45 Å and this revealed predation-associated domain differences to conventional PBP4 housekeeping enzymes (loss of the regulatory domain III, alteration of domain II and a more exposed active site). The Bd3459 active site (and by similarity the Bd0816 active site) can thus accommodate and remodel the various bacterial PGs that Bdellovibrio may encounter across its diverse prey range, compared to the more closed active site that “regular” PBP4s have for self cell wall maintenance. Therefore, during evolution, Bdellovibrio peptidoglycan endopeptidases have adapted into secreted predation-specific proteins, preventing wasteful double invasion, and allowing activity upon the diverse prey peptidoglycan structures to sculpt the prey cell into a stable intracellular niche for replication

Characterisation of cell wall enzymes from Streptococcus pneumoniae

Murein and its turnover products are recognised by components of the innate immune system leading to an inflammatory response and resulting in the killing of bacteria. To counter the clearance by the innate immune system pathogens like Streptococcus pneumoniae have enzymes to modify their cell wall so that they are no longer recognised. The most common modifications are the N-deacetylation and O-acetylation of the glycan strands in the murein. Deacetylated murein was shown to be a poor substrate for lysozyme which is an important factor of the innate immune system capable of lysing sensitive bacteria that have unmodified murein. The single pneumococcal protein responsible for the deacetylation of murein is the murein N- acetylglucosamine deacetylase A (PgdA). Thus PgdA is a possible target for antibacterial therapy. An economical and ease-to-use assay is required to screen for inhibitors of PgdA. Within this work, such an assay has been established using recombinant PgdA with chromogenic substrates. For the first time the activity of purified PgdA with a natural substrate, murein from S. pneumoniae, has been demonstrated. Another interesting candidate as a possible target for inhibitors is the putative murein hydrolase PcsB. However, there are no biochemical data available yet, and in silico comparison and deletion mutants gave only vague hints for a hypothetical function as murein hydrolase. In this work a recombinant, soluble version of PcsB was purified. It showed no significant enzymatic activity against pneumococcal cell wall or murein.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

The Peptidoglycan Sacculus of Myxococcus xanthus Has Unusual Structural Features and Is Degraded during Glycerol-Induced Myxospore Development▿

Upon nutrient limitation cells of the swarming soil bacterium Myxococcus xanthus form a multicellular fruiting body in which a fraction of the cells develop into myxospores. Spore development includes the transition from a rod-shaped vegetative cell to a spherical myxospore and so is expected to be accompanied by changes in the bacterial cell envelope. Peptidoglycan is the shape-determining structure in the cell envelope of most bacteria, including myxobacteria. We analyzed the composition of peptidoglycan isolated from M. xanthus. While the basic structural elements of peptidoglycan in myxobacteria were identical to those in other gram-negative bacteria, the peptidoglycan of M. xanthus had unique structural features. meso- or ll-diaminopimelic acid was present in the stem peptides, and a new modification of N-acetylmuramic acid was detected in a fraction of the muropeptides. Peptidoglycan formed a continuous, bag-shaped sacculus in vegetative cells. The sacculus was degraded during the transition from vegetative cells to glycerol-induced myxospores. The spherical, bag-shaped coats isolated from glycerol-induced spores contained no detectable muropeptides, but they contained small amounts of N-acetylmuramic acid and meso-diaminopimelic acid