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

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.

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

From Quantum Affine Symmetry to Boundary Askey-Wilson Algebra and Reflection Equation

Within the quantum affine algebra representation theory we construct linear covariant operators that generate the Askey-Wilson algebra. It has the property of a coideal subalgebra, which can be interpreted as the boundary symmetry algebra of a model with quantum affine symmetry in the bulk. The generators of the Askey-Wilson algebra are implemented to construct an operator valued $K$- matrix, a solution of a spectral dependent reflection equation. We consider the open driven diffusive system where the Askey-Wilson algebra arises as a boundary symmetry and can be used for an exact solution of the model in the stationary state. We discuss the possibility of a solution beyond the stationary state on the basis of the proposed relation of the Askey-Wilson algebra to the reflection equation

New Molecular Reporters for Rapid Protein Folding Assays

The GFP folding reporter assay [1] uses a C-terminal GFP fusion to report on the folding success of upstream fused polypeptides. The GFP folding assay is widely-used for screening protein variants with improved folding and solubility [2]–[8], but truncation artifacts may arise during evolution, i.e. from de novo internal ribosome entry sites [9]. One way to reduce such artifacts would be to insert target genes within the scaffolding of GFP circular permuted variants. Circular permutants of fluorescent proteins often misfold and are non-fluorescent, and do not readily tolerate fused polypeptides within the fluorescent protein scaffolding [10]–[12]. To overcome these limitations, and to increase the dynamic range for reporting on protein misfolding, we have created eight GFP insertion reporters with different sensitivities to protein misfolding using chimeras of two previously described GFP variants, the GFP folding reporter [1] and the robustly-folding “superfolder” GFP [13]. We applied this technology to engineer soluble variants of Rv0113, a protein from Mycobacterium tuberculosis initially expressed as inclusion bodies in Escherichia coli. Using GFP insertion reporters with increasing stringency for each cycle of mutagenesis and selection led to a variant that produced large amounts of soluble protein at 37°C in Escherichia coli. The new reporter constructs discriminate against truncation artifacts previously isolated during directed evolution of Rv0113 using the original C-terminal GFP folding reporter. Using GFP insertion reporters with variable stringency should prove useful for engineering protein variants with improved folding and solubility, while reducing the number of artifacts arising from internal cryptic ribosome initiation sites

Structural Basis and Catalytic Mechanism for the Dual Functional Endo-β-N-Acetylglucosaminidase A

Endo-β-N-acetylglucosaminidases (ENGases) are dual specificity enzymes with an ability to catalyze hydrolysis and transglycosylation reactions. Recently, these enzymes have become the focus of intense research because of their potential for synthesis of glycopeptides. We have determined the 3D structures of an ENGase from Arthrobacter protophormiae (Endo-A) in 3 forms, one in native form, one in complex with Man3GlcNAc-thiazoline and another in complex with GlcNAc-Asn. The carbohydrate moiety sits above the TIM-barrel in a cleft region surrounded by aromatic residues. The conserved essential catalytic residues – E173, N171 and Y205 are within hydrogen bonding distance of the substrate. W216 and W244 regulate access to the active site during transglycosylation by serving as “gate-keepers”. Interestingly, Y299F mutation resulted in a 3 fold increase in the transglycosylation activity. The structure provides insights into the catalytic mechanism of GH85 family of glycoside hydrolases at molecular level and could assist rational engineering of ENGases