A family of tridiagonal pairs and related symmetric functions

A family of tridiagonal pairs which appear in the context of quantum integrable systems is studied in details. The corresponding eigenvalue sequences, eigenspaces and the block tridiagonal structure of their matrix realizations with respect the dual eigenbasis are described. The overlap functions between the two dual basis are shown to satisfy a coupled system of recurrence relations and a set of discrete second-order $q-$difference equations which generalize the ones associated with the Askey-Wilson orthogonal polynomials with a discrete argument. Normalizing the fundamental solution to unity, the hierarchy of solutions are rational functions of one discrete argument, explicitly derived in some simplest examples. The weight function which ensures the orthogonality of the system of rational functions defined on a discrete real support is given.Comment: 17 pages; LaTeX file with amssymb. v2: few minor changes, to appear in J.Phys.A; v3: Minor misprints, eq. (48) and orthogonality condition corrected compared to published versio

LU factorizations, q=0 limits, and p-adic interpretations of some q-hypergeometric orthogonal polynomials

For little q-Jacobi polynomials and q-Hahn polynomials we give particular q-hypergeometric series representations in which the termwise q=0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as LU factorizations. We develop a general theory of LU factorizations related to complete systems of orthogonal polynomials with discrete orthogonality relations which admit a dual system of orthogonal polynomials. For the q=0 orthogonal limit functions we discuss interpretations on p-adic spaces. In the little 0-Jacobi case we also discuss product formulas.Comment: changed title, references updated, minor changes matching the version to appear in Ramanujan J.; 22 p

Central extension of the reflection equations and an analog of Miki's formula

Two different types of centrally extended quantum reflection algebras are introduced. Realizations in terms of the elements of the central extension of the Yang-Baxter algebra are exhibited. A coaction map is identified. For the special case of $U_q(\hat{sl_2})$, a realization in terms of elements satisfying the Zamolodchikov-Faddeev algebra - a `boundary' analog of Miki's formula - is also proposed, providing a free field realization of $O_q(\hat{sl_2})$ (q-Onsager) currents.Comment: 11 pages; two references added; to appear in J. Phys.

SAGA: A project to automate the management of software production systems

The project to automate the management of software production systems is described. The SAGA system is a software environment that is designed to support most of the software development activities that occur in a software lifecycle. The system can be configured to support specific software development applications using given programming languages, tools, and methodologies. Meta-tools are provided to ease configuration. Several major components of the SAGA system are completed to prototype form. The construction methods are described

Structure of HrcQ(B)-C, a conserved component of the bacterial type III secretion systems

Type III secretion systems enable plant and animal bacterial pathogens to deliver virulence proteins into the cytosol of eukaryotic host cells, causing a broad spectrum of diseases including bacteremia, septicemia, typhoid fever, and bubonic plague in mammals, and localized lesions, systemic wilting, and blights in plants. In addition, type III secretion systems are also required for biogenesis of the bacterial flagellum. The HrcQ(B) protein, a component of the secretion apparatus of Pseudomonas syringae with homologues in all type III systems, has a variable N-terminal and a conserved C-terminal domain (HrcQ(B)-C). Here, we report the crystal structure of HrcQ(B)-C and show that this domain retains the ability of the full-length protein to interact with other type III components. A 3D analysis of sequence conservation patterns reveals two clusters of residues potentially involved in protein–protein interactions. Based on the analogies between HrcQ(B) and its flagellum homologues, we propose that HrcQ(B)-C participates in the formation of a C-ring-like assembly

A deformed analogue of Onsager's symmetry in the XXZ open spin chain

The XXZ open spin chain with general integrable boundary conditions is shown to possess a q-deformed analogue of the Onsager's algebra as fundamental non-abelian symmetry which ensures the integrability of the model. This symmetry implies the existence of a finite set of independent mutually commuting nonlocal operators which form an abelian subalgebra. The transfer matrix and local conserved quantities, for instance the Hamiltonian, are expressed in terms of these nonlocal operators. It follows that Onsager's original approach of the planar Ising model can be extended to the XXZ open spin chain.Comment: 12 pages; LaTeX file with amssymb; v2: typos corrected, clarifications in the text; v3: minor changes in references, version to appear in JSTA

Structure of the Mg-Chelatase Cofactor GUN4 Reveals a Novel Hand-Shaped Fold for Porphyrin Binding

In plants, the accumulation of the chlorophyll precursor Mg-protoporphyrin IX (Mg-Proto) in the plastid regulates the expression of a number of nuclear genes with functions related to photosynthesis. Analysis of the plastid-to-nucleus signaling activity of Mg-Proto in Arabidopsis thaliana led to the discovery of GUN4, a novel porphyrin-binding protein that also dramatically enhances the activity of Mg-chelatase, the enzyme that synthesizes Mg-Proto. GUN4 may also play a role in both photoprotection and the cellular shuttling of tetrapyrroles. Here we report a 1.78-Å resolution crystal structure of Synechocystis GUN4, in which the porphyrin-binding domain adopts a unique three dimensional fold with a “cupped hand” shape. Biophysical and biochemical analyses revealed the specific site of interaction between GUN4 and Mg-Proto and the energetic determinants for the GUN4 • Mg-Proto interaction. Our data support a novel protective function for GUN4 in tetrapyrrole trafficking. The combined structural and energetic analyses presented herein form the physical-chemical basis for understanding GUN4 biological activity, including its role in the stimulation of Mg-chelatase activity, as well as in Mg-Proto retrograde signaling

Adaptive response and enlargement of dynamic range

Many membrane channels and receptors exhibit adaptive, or desensitized, response to a strong sustained input stimulus, often supported by protein activity-dependent inactivation. Adaptive response is thought to be related to various cellular functions such as homeostasis and enlargement of dynamic range by background compensation. Here we study the quantitative relation between adaptive response and background compensation within a modeling framework. We show that any particular type of adaptive response is neither sufficient nor necessary for adaptive enlargement of dynamic range. In particular a precise adaptive response, where system activity is maintained at a constant level at steady state, does not ensure a large dynamic range neither in input signal nor in system output. A general mechanism for input dynamic range enlargement can come about from the activity-dependent modulation of protein responsiveness by multiple biochemical modification, regardless of the type of adaptive response it induces. Therefore hierarchical biochemical processes such as methylation and phosphorylation are natural candidates to induce this property in signaling systems.Comment: Corrected typos, minor text revision

The Erd\H{o}s-Ko-Rado theorem for twisted Grassmann graphs

We present a "modern" approach to the Erd\H{o}s-Ko-Rado theorem for Q-polynomial distance-regular graphs and apply it to the twisted Grassmann graphs discovered in 2005 by van Dam and Koolen.Comment: 5 page

Crystal structure of Hop2-Mnd1 and mechanistic insights into its role in meiotic recombination

In meiotic DNA recombination, the Hop2-Mnd1 complex promotes Dmc1-mediated single-stranded DNA (ssDNA) invasion into homologous chromosomes to form a synaptic complex by a yet-unclear mechanism. Here, the crystal structure of Hop2-Mnd1 reveals that it forms a curved rod-like structure consisting of three leucine zippers and two kinked junctions. One end of the rod is linked to two juxtaposed winged-helix domains, and the other end is capped by extra ?-helices to form a helical bundle-like structure. Deletion analysis shows that the helical bundle-like structure is sufficient for interacting with the Dmc1-ssDNA nucleofilament, and molecular modeling suggests that the curved rod could be accommodated into the helical groove of the nucleofilament. Remarkably, the winged-helix domains are juxtaposed at fixed relative orientation, and their binding to DNA is likely to perturb the base pairing according to molecular simulations. These findings allow us to propose a model explaining how Hop2-Mnd1 juxtaposes Dmc1-bound ssDNA with distorted recipient double-stranded DNA and thus facilitates strand invasion