Parametric Representation of Rank d Tensorial Group Field Theory: Abelian Models with Kinetic Term ∑s∣ps∣+μ\sum_{s}|p_s| + \mu

We consider the parametric representation of the amplitudes of Abelian models in the so-called framework of rank $d$ Tensorial Group Field Theory. These models are called Abelian because their fields live on $U(1)^D$. We concentrate on the case when these models are endowed with particular kinetic terms involving a linear power in momenta. New dimensional regularization and renormalization schemes are introduced for particular models in this class: a rank 3 tensor model, an infinite tower of matrix models $\phi^{2n}$ over $U(1)$, and a matrix model over $U(1)^2$. For all divergent amplitudes, we identify a domain of meromorphicity in a strip determined by the real part of the group dimension $D$. From this point, the ordinary subtraction program is applied and leads to convergent and analytic renormalized integrals. Furthermore, we identify and study in depth the Symanzik polynomials provided by the parametric amplitudes of generic rank $d$ Abelian models. We find that these polynomials do not satisfy the ordinary Tutte's rules (contraction/deletion). By scrutinizing the "face"-structure of these polynomials, we find a generalized polynomial which turns out to be stable only under contraction.Comment: 69 pages, 35 figure

Quantum Mechanics on SO(3) via Non-commutative Dual Variables

We formulate quantum mechanics on SO(3) using a non-commutative dual space representation for the quantum states, inspired by recent work in quantum gravity. The new non-commutative variables have a clear connection to the corresponding classical variables, and our analysis confirms them as the natural phase space variables, both mathematically and physically. In particular, we derive the first order (Hamiltonian) path integral in terms of the non-commutative variables, as a formulation of the transition amplitudes alternative to that based on harmonic analysis. We find that the non-trivial phase space structure gives naturally rise to quantum corrections to the action for which we find a closed expression. We then study both the semi-classical approximation of the first order path integral and the example of a free particle on SO(3). On the basis of these results, we comment on the relevance of similar structures and methods for more complicated theories with group-based configuration spaces, such as Loop Quantum Gravity and Spin Foam models.Comment: 29 pages; matches the published version plus footnote 7, a journal reference include

Structure of transmembrane prolyl 4-hydroxylase reveals unique organization of EF and dioxygenase domains

Prolyl 4-hydroxylases (P4Hs) catalyze post-translational hydroxylation of peptidyl proline residues. In addition to collagen P4Hs and hypoxia-inducible factor P4Hs, a third P4H—the poorly characterized endoplasmic reticulum–localized transmembrane prolyl 4-hydroxylase (P4H-TM)—is found in animals. P4H-TM variants are associated with the familiar neurological HIDEA syndrome, but how these variants might contribute to disease is unknown. Here, we explored this question in a structural and functional analysis of soluble human P4H-TM. The crystal structure revealed an EF domain with two Ca2+-binding motifs inserted within the catalytic domain. A substrate-binding groove was formed between the EF domain and the conserved core of the catalytic domain. The proximity of the EF domain to the active site suggests that Ca2+ binding is relevant to the catalytic activity. Functional analysis demonstrated that Ca2+-binding affinity of P4H-TM is within the range of physiological Ca2+ concentration in the endoplasmic reticulum. P4H-TM was found both as a monomer and a dimer in the solution, but the monomer–dimer equilibrium was not regulated by Ca2+. The catalytic site contained bound Fe2+ and N-oxalylglycine, which is an analogue of the cosubstrate 2-oxoglutarate. Comparison with homologous P4H structures complexed with peptide substrates showed that the substrate-interacting residues and the lid structure that folds over the substrate are conserved in P4H-TM, whereas the extensive loop structures that surround the substrate-binding groove, generating a negative surface potential, are different. Analysis of the structure suggests that the HIDEA variants cause loss of P4H-TM function. In conclusion, P4H-TM shares key structural elements with other P4Hs while having a unique EF domain.publishedVersio

Structural similarities and functional differences clarify evolutionary relationships between tRNA healing enzymes and the myelin enzyme CNPase

Abstract Background: Eukaryotic tRNA splicing is an essential process in the transformation of a primary tRNA transcript into a mature functional tRNA molecule. 5′-phosphate ligation involves two steps: a healing reaction catalyzed by polynucleotide kinase (PNK) in association with cyclic phosphodiesterase (CPDase), and a sealing reaction catalyzed by an RNA ligase. The enzymes that catalyze tRNA healing in yeast and higher eukaryotes are homologous to the members of the 2H phosphoesterase superfamily, in particular to the vertebrate myelin enzyme 2′,3′-cyclic nucleotide 3′-phosphodiesterase (CNPase). Results: We employed different biophysical and biochemical methods to elucidate the overall structural and functional features of the tRNA healing enzymes yeast Trl1 PNK/CPDase and lancelet PNK/CPDase and compared them with vertebrate CNPase. The yeast and the lancelet enzymes have cyclic phosphodiesterase and polynucleotide kinase activity, while vertebrate CNPase lacks PNK activity. In addition, we also show that the healing enzymes are structurally similar to the vertebrate CNPase by applying synchrotron radiation circular dichroism spectroscopy and small-angle X-ray scattering. Conclusions: We provide a structural analysis of the tRNA healing enzyme PNK and CPDase domains together. Our results support evolution of vertebrate CNPase from tRNA healing enzymes with a loss of function at its N-terminal PNK-like domain