Quantum Kaleidoscopes and Bell's theorem

A quantum kaleidoscope is defined as a set of observables, or states, consisting of many different subsets that provide closely related proofs of the Bell-Kochen-Specker (BKS) and Bell nonlocality theorems. The kaleidoscopes prove the BKS theorem through a simple parity argument, which also doubles as a proof of Bell's nonlocality theorem if use is made of the right sort of entanglement. Three closely related kaleidoscopes are introduced and discussed in this paper: a 15-observable kaleidoscope, a 24-state kaleidoscope and a 60-state kaleidoscope. The close relationship of these kaleidoscopes to a configuration of 12 points and 16 lines known as Reye's configuration is pointed out. The "rotations" needed to make each kaleidoscope yield all its apparitions are laid out. The 60-state kaleidoscope, whose underlying geometrical structure is that of ten interlinked Reye's configurations (together with their duals), possesses a total of 1120 apparitions that provide proofs of the two Bell theorems. Some applications of these kaleidoscopes to problems in quantum tomography and quantum state estimation are discussed.Comment: Two new references (No. 21 and 22) to related work have been adde

Characterization of Binary Constraint System Games

We consider a class of nonlocal games that are related to binary constraint systems (BCSs) in a manner similar to the games implicit in the work of Mermin [N.D. Mermin, "Simple unified form for the major no-hidden-variables theorems," Phys. Rev. Lett., 65(27):3373-3376, 1990], but generalized to n binary variables and m constraints. We show that, whenever there is a perfect entangled protocol for such a game, there exists a set of binary observables with commutations and products similar to those exhibited by Mermin. We also show how to derive upper bounds strictly below 1 for the the maximum entangled success probability of some BCS games. These results are partial progress towards a larger project to determine the computational complexity of deciding whether a given instance of a BCS game admits a perfect entangled strategy or not.Comment: Revised version corrects an error in the previous version of the proof of Theorem 1 that arises in the case of POVM measurement

Predicted class-I aminoacyl tRNA synthetase-like proteins in non-ribosomal peptide synthesis

<p>Abstract</p> <p>Background</p> <p>Recent studies point to a great diversity of non-ribosomal peptide synthesis systems with major roles in amino acid and co-factor biosynthesis, secondary metabolism, and post-translational modifications of proteins by peptide tags. The least studied of these systems are those utilizing tRNAs or aminoacyl-tRNA synthetases (AAtRS) in non-ribosomal peptide ligation.</p> <p>Results</p> <p>Here we describe novel examples of AAtRS related proteins that are likely to be involved in the synthesis of widely distributed peptide-derived metabolites. Using sensitive sequence profile methods we show that the cyclodipeptide synthases (CDPSs) are members of the HUP class of Rossmannoid domains and are likely to be highly derived versions of the class-I AAtRS catalytic domains. We also identify the first eukaryotic CDPSs in fungi and in animals; they might be involved in immune response in the latter organisms. We also identify a paralogous version of the methionyl-tRNA synthetase, which is widespread in bacteria, and present evidence using contextual information that it might function independently of protein synthesis as a peptide ligase in the formation of a peptide- derived secondary metabolite. This metabolite is likely to be heavily modified through multiple reactions catalyzed by a metal-binding cupin domain and a lysine N6 monooxygenase that are strictly associated with this paralogous methionyl-tRNA synthetase (MtRS). We further identify an analogous system wherein the MtRS has been replaced by more typical peptide ligases with the ATP-grasp or modular condensation-domains.</p> <p>Conclusions</p> <p>The prevalence of these predicted biosynthetic pathways in phylogenetically distant, pathogenic or symbiotic bacteria suggests that metabolites synthesized by them might participate in interactions with the host. More generally, these findings point to a complete spectrum of recruitment of AAtRS to various non-ribosomal biosynthetic pathways, ranging from the conventional AAtRS, through closely related paralogous AAtRS dedicated to certain pathways, to highly derived versions of the class-I AAtRS catalytic domain like the CDPSs. Both the conventional AAtRS and their closely related paralogs often provide aminoacylated tRNAs for peptide ligations by MprF/Fem/MurM-type acetyltransferase fold ligases in the synthesis of peptidoglycan, N-end rule modifications of proteins, lipid aminoacylation or biosynthesis of antibiotics, such as valinamycin. Alternatively they might supply aminoacylated tRNAs for other biosynthetic pathways like that for tetrapyrrole or directly function as peptide ligases as in the case of mycothiol and those identified here.</p> <p>Reviewers</p> <p>This article was reviewed by Andrei Osterman and Igor Zhulin.</p

Application of comparative genomics in the identification and analysis of novel families of membrane-associated receptors in bacteria

BACKGROUND: A great diversity of multi-pass membrane receptors, typically with 7 transmembrane (TM) helices, is observed in the eukaryote crown group. So far, they are relatively rare in the prokaryotes, and are restricted to the well-characterized sensory rhodopsins of various phototropic prokaryotes. RESULTS: Utilizing the currently available wealth of prokaryotic genomic sequences, we set up a computational screen to identify putative 7 (TM) and other multi-pass membrane receptors in prokaryotes. As a result of this procedure we were able to recover two widespread families of 7 TM receptors in bacteria that are distantly related to the eukaryotic 7 TM receptors and prokaryotic rhodopsins. Using sequence profile analysis, we were able to establish that the first members of these receptor families contain one of two distinct N-terminal extracellular globular domains, which are predicted to bind ligands such as carbohydrates. In their intracellular portions they contain fusions to a variety of signaling domains, which suggest that they are likely to transduce signals via cyclic AMP, cyclic diguanylate, histidine phosphorylation, dephosphorylation, and through direct interactions with DNA. The second family of bacterial 7 TM receptors possesses an α-helical extracellular domain, and is predicted to transduce a signal via an intracellular HD hydrolase domain. Based on comparative analysis of gene neighborhoods, this receptor is predicted to function as a regulator of the diacylglycerol-kinase-dependent glycerolipid pathway. Additionally, our procedure also recovered other types of putative prokaryotic multi-pass membrane associated receptor domains. Of these, we characterized two widespread, evolutionarily mobile multi-TM domains that are fused to a variety of C-terminal intracellular signaling domains. One of these typified by the Gram-positive LytS protein is predicted to be a potential sensor of murein derivatives, whereas the other one typified by the Escherichia coli UhpB protein is predicted to function as sensor of conformational changes occurring in associated membrane proteins CONCLUSIONS: We present evidence for considerable variety in the types of uncharacterized surface receptors in bacteria, and reconstruct the evolutionary processes that model their diversity. The identification of novel receptor families in prokaryotes is likely to aid in the experimental analysis of signal transduction and environmental responses of several bacteria, including pathogens such as Leptospira, Treponema, Corynebacterium, Coxiella, Bacillus anthracis and Cytophaga

Evolutionary history, structural features and biochemical diversity of the NlpC/P60 superfamily of enzymes

BACKGROUND: Peptidoglycan is hydrolyzed by a diverse set of enzymes during bacterial growth, development and cell division. The N1pC/P60 proteins define a family of cell-wall peptidases that are widely represented in various bacterial lineages. Currently characterized members are known to hydrolyze D-γ-glutamyl-meso-diaminopimelate or N-acetylmuramate-L-alanine linkages. RESULTS: Detailed analysis of the N1pC/P60 peptidases showed that these proteins define a large superfamily encompassing several diverse groups of proteins. In addition to the well characterized P60-like proteins, this superfamily includes the AcmB/LytN and YaeF/YiiX families of bacterial proteins, the amidase domain of bacterial and kinetoplastid glutathionylspermidine synthases (GSPSs), and several proteins from eukaryotes, phages, poxviruses, positive-strand RNA viruses, and certain archaea. The eukaryotic members include lecithin retinol acyltransferase (LRAT), nematode developmental regulator Egl-26, and candidate tumor suppressor H-rev107. These eukaryotic proteins, along with the bacterial YaeF/poxviral G6R family, show a circular permutation of the catalytic domain. We identified three conserved residues, namely a cysteine, a histidine and a polar residue, that are involved in the catalytic activities of this superfamily. Evolutionary analysis of this superfamily shows that it comprises four major families, with diverse domain architectures in each of them. CONCLUSIONS: Several related, but distinct, catalytic activities, such as murein degradation, acyl transfer and amide hydrolysis, have emerged in the N1pC/P60 superfamily. The three conserved catalytic residues of this superfamily are shown to be equivalent to the catalytic triad of the papain-like thiol peptidases. The predicted structural features indicate that the N1pC/P60 enzymes contain a fold similar to the papain-like peptidases, transglutaminases and arylamine acetyltransferases