A Groenewold-Van Hove Theorem for S^2

We prove that there does not exist a nontrivial quantization of the Poisson algebra of the symplectic manifold S^2 which is irreducible on the subalgebra generated by the components {S_1,S_2,S_3} of the spin vector. We also show that there does not exist such a quantization of the Poisson subalgebra P consisting of polynomials in {S_1,S_2,S_3}. Furthermore, we show that the maximal Poisson subalgebra of P containing {1,S_1,S_2,S_3} that can be so quantized is just that generated by {1,S_1,S_2,S_3}.Comment: 20 pages, AMSLaTe

Constrained Dynamics for Quantum Mechanics I. Restricting a Particle to a Surface

We analyze constrained quantum systems where the dynamics do not preserve the constraints. This is done in particular for the restriction of a quantum particle in Euclidean n-space to a curved submanifold, and we propose a method of constraining and dynamics adjustment which produces the right Hamiltonian on the submanifold when tested on known examples. This method we hope will become the germ of a full Dirac algorithm for quantum constraints. We take a first step in generalising it to the situation where the constraint is a general selfadjoint operator with some additional structures.Comment: 49 pages, TEX, input files amssym.def, amssym.te

Identification of a lipoteichoic acid glycosyltransferase enzyme reveals that GW-domain containing proteins can be retained in the cell wall of Listeria monocytogenes in the absence of lipoteichoic acid or its modifications

Listeria monocytogenes is a foodborne Gram-positive bacterial pathogen, and many of its virulence factors are either secreted proteins or proteins covalently or noncovalently attached to the cell wall. Previous work has indicated that noncovalently attached proteins with GW (glycine-tryptophan) domains are retained in the cell wall by binding to the cell wall polymer lipoteichoic acid (LTA). LTA is a glycerol phosphate polymer, which is modified in L. monocytogenes with galactose and d-alanine residues. We identified Lmo0933 as the cytoplasmic glycosyltransferase required for the LTA glycosylation process and renamed the protein GtlA, for glycosyltransferase LTA A Using L. monocytogenes mutants lacking galactose or d-alanine modifications or the complete LTA polymer, we show that GW domain proteins are retained within the cell wall, indicating that other cell wall polymers are involved in the retention of GW domain proteins. Further experiments revealed peptidoglycan as the binding receptor as a purified GW domain fusion protein can bind to L. monocytogenes cells lacking wall teichoic acid (WTA) as well as purified peptidoglycan derived from a wild-type or WTA-negative strain. With this, we not only identify the first enzyme involved in the LTA glycosylation process, but we also provide new insight into the binding mechanism of noncovalently attached cell wall proteins.Over the past 20 years, a large number of bacterial genome sequences have become available. Computational approaches are used for the genome annotation and identification of genes and encoded proteins. However, the function of many proteins is still unknown and often cannot be predicted bioinformatically. Here, we show that the previously uncharacterized Listeria monocytogenes gene lmo0933 likely codes for a glycosyltransferase required for the decoration of the cell wall polymer lipoteichoic acid (LTA) with galactose residues. Using L. monocytogenes mutants lacking LTA modifications or the complete polymer, we show that specific cell wall proteins, often associated with virulence, are retained within the cell wall, indicating that additional cell wall polymers are involved in their retention

ppGpp negatively impacts ribosome assembly affecting growth and antimicrobial tolerance in Gram-positive bacteria

The stringent response is a survival mechanism used by bacteria to deal with stress. It is coordinated by the nucleotides guanosine tetraphosphate and pentaphosphate [(p)ppGpp], which interact with target proteins to promote bacterial survival. Although this response has been well characterized in proteobacteria, very little is known about the effectors of this signaling system in Gram-positive species. Here, we report on the identification of seven target proteins for the stringent response nucleotides in the Gram-positive bacterium Staphylococcus aureus. We demonstrate that the GTP synthesis enzymes HprT and Gmk bind with a high affinity, leading to an inhibition of GTP production. In addition, we identified five putative GTPases—RsgA, RbgA, Era, HflX, and ObgE—as (p)ppGpp target proteins. We show that RsgA, RbgA, Era, and HflX are functional GTPases and that their activity is promoted in the presence of ribosomes but strongly inhibited by the stringent response nucleotides. By characterizing the function of RsgA in vivo, we ascertain that this protein is involved in ribosome assembly, with an rsgA deletion strain, or a strain inactivated for GTPase activity, displaying decreased growth, a decrease in the amount of mature 70S ribosomes, and an increased level of tolerance to antimicrobials. We additionally demonstrate that the interaction of ppGpp with cellular GTPases is not unique to the staphylococci, as homologs from Bacillus subtilis and Enterococcus faecalis retain this ability. Taken together, this study reveals ribosome inactivation as a previously unidentified mechanism through which the stringent response functions in Gram-positive bacteria

Inactivation of the monofunctional peptidoglycan glycosyltransferase SgtB allows Staphylococcus aureus to survive in the absence of lipoteichoic acid

The cell wall of Staphylococcus aureus is composed of peptidoglycan and the anionic polymers lipoteichoic acid (LTA) and wall teichoic acid. LTA is required for growth and normal cell morphology in S. aureus. Strains lacking LTA are usually viable only when grown under osmotically stabilizing conditions or after the acquisition of compensatory mutations. LTA-negative suppressor strains with inactivating mutations in gdpP, which resulted in increased intracellular c-di-AMP levels, were described previously. Here, we sought to identify factors other than c-di-AMP that allow S. aureus to survive without LTA. LTA-negative strains able to grow in unsupplemented medium were obtained and found to contain mutations in sgtB, mazE, clpX, or vraT. The growth improvement through mutations in mazE and sgtB was confirmed by complementation analysis. We also showed that an S. aureus sgtB transposon mutant, with the monofunctional peptidoglycan glycosyltransferase SgtB inactivated, displayed a 4-fold increase in the MIC of oxacillin, suggesting that alterations in the peptidoglycan structure could help bacteria compensate for the lack of LTA. Muropeptide analysis of peptidoglycans isolated from a wild-type strain and sgtB mutant strain did not reveal any sizable alterations in the peptidoglycan structure. In contrast, the peptidoglycan isolated from an LTA-negative ltaS mutant strain showed a significant reduction in the fraction of highly cross-linked peptidoglycan, which was partially rescued in the sgtB ltaS double mutant suppressor strain. Taken together, these data point toward an important function of LTA in cell wall integrity through its necessity for proper peptidoglycan assembly

Identification of the main glutamine and glutamate transporters in Staphylococcus aureus and their impact on c-di-AMP production

A Staphylococcus aureus strain deleted for the c‐di‐AMP cyclase gene dacA is unable to survive in rich medium unless it acquires compensatory mutations. Previously identified mutations were in opuD, encoding the main glycine‐betaine transporter, and alsT, encoding a predicted amino acid transporter. Here, we show that inactivation of OpuD restores the cell size of a dacA mutant to near wild‐type (WT) size, while inactivation of AlsT does not. AlsT was identified as an efficient glutamine transporter, indicating that preventing glutamine uptake in rich medium rescues the growth of the S. aureus dacA mutant. In addition, GltS was identified as a glutamate transporter. By performing growth curves with WT, alsT and gltS mutant strains in defined medium supplemented with ammonium, glutamine or glutamate, we revealed that ammonium and glutamine, but not glutamate promote the growth of S. aureus. This suggests that besides ammonium also glutamine can serve as a nitrogen source under these conditions. Ammonium and uptake of glutamine via AlsT and hence likely a higher intracellular glutamine concentration inhibited c‐di‐AMP production, while glutamate uptake had no effect. These findings provide, besides the previously reported link between potassium and osmolyte uptake, a connection between nitrogen metabolism and c‐di‐AMP signalling in S. aureus

Mathematical structure of the temporal gauge

The mathematical structure of the temporal gauge of QED is critically examined in both the alternative formulations characterized by either positivity or regularity of the Weyl algebra. The conflict between time translation invariance and Gauss law constraint is shown to lead to peculiar features. In the positive case only the correlations of exponentials of fields exist (non regularity), the space translations are not strongly continuous, so that their generators do not exist, a theta vacuum degeneracy occurs, associated to a spontaneous symmetry breaking. In the indefinite case the spectral condition only holds in terms of positivity of the energy, gauge invariant theta-vacua exist on the observables, with no extension to time translation invariant states on the field algebra, the vacuum is faithful on the longitudinal algebra and a KMS structure emerges. Functional integral representations are derived in both cases, with the alternative between ergodic measures on real random fields or complex Gaussian random fields.Comment: Late

The second messenger c-di-AMP inhibits the osmolyte uptake system OpuC in Staphylococcus aureus

Staphylococcus aureus is an important opportunistic human pathogen that is highly resistant to osmotic stresses. In order to survive an increase in osmolarity, bacteria immediately take up potassium and small organic compounds, also referred to as compatible solutes. The second messenger c-di-AMP binds to several receptor proteins, most of which are involved in ion and potassium uptake, that help bacteria cope with osmotic stress. In this study, we identified OpuCA, the ATPase component of an uptake system for the compatible solute carnitine, as a cdi-AMP target protein in S. aureus and found that a strain overproducing c-di-AMP showed reduced carnitine uptake. The CBS domains of OpuCA bound to c-di-AMP, and a crystal structure revealed a putative binding pocket for c-di-AMP in the cleft between the two CBS domains. Thus, c-di-AMP is involved in regulating both branches of osmoprotection (potassium uptake and compatible solute uptake), suggesting that c-di-AMP is a general osmotic stress regulato