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Recently, we found Mellin–Barnes integrals, representing the wave function for $GL(n,{\mathbb {R}})$ hyperbolic Sutherland model. In present paper, we establish bispectral properties of this wave function with respect to dual Ruijesenaars–Macdonald operators.

We obtain certain Mellin–Barnes integrals that present wave functions for $GL(n,{\mathbb {R}})$ hyperbolic Sutherland model with arbitrary positive coupling constant.

Characterizing a cancer spliceosome Cells undergo many genomic changes as they progress toward metastatic cancer. One aspect of this change is to RNA expression and splicing isoforms, but how these differences affect tumor progression is not well characterized. Fish et al. developed a computational framework called pyTEISER that identifies structural cis-regulatory elements that control diverse types of RNA regulation. Applying pyTEISER to models of breast cancer metastasis, they discovered an RNA short-stem-loop element that forms a “structural splicing enhancer” that acts in cis to regulate alternative splicing of RNA transcripts. One of these interactions encompasses the RNA-binding protein SNRPA1 and results in alternative exon inclusion that affects metastatic capacity in xenograft models. Thus, RNA element binding may play a role in splicing regulation and is potentially an important component of the cis-splicing code. Science , this issue p. eabc7531

Although the primary protein sequence of ubiquitin (Ub) is extremely stable over evolutionary time, it is highly tolerant to mutation during selection experiments performed in the laboratory. We have proposed that this discrepancy results from the difference between fitness under laboratory culture conditions and the selective pressures in changing environments over evolutionary timescales. Building on our previous work (Mavor et al., 2016), we used deep mutational scanning to determine how twelve new chemicals (3-Amino-1,2,4-triazole, 5-fluorocytosine, Amphotericin B, CaCl2, Cerulenin, Cobalt Acetate, Menadione, Nickel Chloride, p-Fluorophenylalanine, Rapamycin, Tamoxifen, and Tunicamycin) reveal novel mutational sensitivities of ubiquitin residues. Collectively, our experiments have identified eight new sensitizing conditions for Lys63 and uncovered a sensitizing condition for every position in Ub except Ser57 and Gln62. By determining the ubiquitin fitness landscape under different chemical constraints, our work helps to resolve the inconsistencies between deep mutational scanning experiments and sequence conservation over evolutionary timescales., Summary: We organized a project-based course that used deep mutational scanning of ubiquitin to resolve the inconsistencies between tolerance to mutations in laboratory conditions and sequence conservation over evolutionary timescales.

Although the primary protein sequence of ubiquitin (Ub) is extremely stable over evolutionary time, it is highly tolerant to mutation during selection experiments performed in the laboratory. We have proposed that this discrepancy results from the difference between fitness under laboratory culture conditions and the selective pressures in changing environments over evolutionary time scales. Building on our previous work (Mavor et al 2016), we used deep mutational scanning to determine how twelve new chemicals (3-Amino-1,2,4-triazole, 5-fluorocytosine, Amphotericin B, CaCl2, Cerulenin, Cobalt Acetate, Menadione, Nickel Chloride, p-fluorophenylalanine, Rapamycin, Tamoxifen, and Tunicamycin) reveal novel mutational sensitivities of ubiquitin residues. We found sensitization of Lys63 in eight new conditions. In total, our experiments have uncovered a sensitizing condition for every position in Ub except Ser57 and Gln62. By determining the Ubiquitin fitness landscape under different chemical constraints, our work helps to resolve the inconsistencies between deep mutational scanning experiments and sequence conservation over evolutionary timescales.Builds onMavor D, Barlow KA, Thompson S, Barad BA, Bonny AR, Cario CL, Gaskins G, Liu Z, Deming L, Axen SD, Caceres E, Chen W, Cuesta A, Gate R, Green EM, Hulce KR, Ji W, Kenner LR, Mensa B, Morinishi LS, Moss SM, Mravic M, Muir RK, Niekamp S, Nnadi CI, Palovcak E, Poss EM, Ross TD, Salcedo E, See S, Subramaniam M, Wong AW, Li J, Thorn KS, Conchúir SÓ, Roscoe BP, Chow ED, DeRisi JL, Kortemme T, Bolon DN, Fraser JS. Determination of Ubiquitin Fitness Landscapes Under Different Chemical Stresses in a Classroom Setting. eLife. 2016.Impact StatementWe organized a project-based course that used deep mutational scanning in multiple chemical conditions to resolve the inconsistencies between tolerance to mutations in laboratory conditions and sequence conservation over evolutionary timescales.

Diet shapes host and gut microbe fitness The human gut microbiota is hugely diverse, with many strain variants having a multiplicity of effects on host metabolism and immunity. To define some of these functions, Wu et al. made libraries of mutants of Bacteroides species known for their capacity to process otherwise intractable dietary fiber. Germ-free mice colonized with defined gut microbiota communities containing the mutants were fed specific diets containing different ratios of fat and fiber. Genes, strains, and species were identified that were associated with specific metabolic pathways. The community responses to dietary shifts were manipulated in an attempt to characterize species for their probiotic or therapeutic potential. Science , this issue 10.1126/science.aac5992 >

The factorization of the universal R-matrix corresponding to the so-called Drinfeld Hopf structure is described in the example of the quantum affine algebra $$U_q \left( {\hat sl_2 } \right)$$ . As a result of the factorization procedure, we deduce certain differential equations on the factors of the universal R-matrix that allow uniquely constructing these factors in the integral form.

The goal of this paper is to analyse the method of angular quantization for the Sine-Gordon model at the free fermion point, which is one of the most investigated models of the two-dimensional integrable field theories. The angular quantization method (see hep-th/9707091) is a continuous analog of the Baxter’s corner transfer matrix method. Investigating the canonical quantization of the free massive Dirac fermions in one Rindler wedge we identify this quantization with a representation of the infinitedimensional algebra introduced in the paper q-alg/9702002 and specialized to the free fermion point. We construct further the main ingredients of the SG theory in terms of the representation theory of this algebra following the approach by M.Jimbo, T.Miwa et al.

The classical limit of the scaled elliptic algebra A((h) over bar eta)( (2)) is investigated. The limiting Lie algebra is described in two equivalent ways: as a central extension of the algebra of generalized automorphic sl(2) valued functions on a strip and as an extended algebra of decreasing automorphic sl(2) valued functions on the real line. A bialgebra structure and an infinite-dimensional representation in the Fock space are studied. The classical limit of elliptic algebra A(q,p)( (2)) is also briefly presented.

The classical limit of the scaled elliptic algebra \(\mathcal{A}\) ħ,η (\(\widetilde{\mathfrak{s}\mathfrak{l}}_2\)) is investigated. The limiting Lie algebra is described in two equivalent ways: as a central extension of the algebra of generalized automorphic sl2 valued functions on a strip and as an extended algebra of decreasing automorphic sl2 valued functions on the real line. A bialgebra structure and an infinite-dimensional representation in the Fock space are studied. The classical limit of elliptic algebra \(\mathcal{A}\)q,p (\(\widetilde{\mathfrak{s}\mathfrak{l}}_2\)) is also briefly presented.

It is known that symmetric orbits in ${\bf g}^*$ for any simple Lie algebra ${\bf g}$ are equiped with a Poisson pencil generated by the Kirillov-Kostant-Souriau bracket and the reduced Sklyanin bracket associated to the "canonical" R-matrix. We realize quantization of this Poisson pencil on $\cp$ type orbits (i.e. orbits in $sl(n+1)^*$ whose real compact form is $ CP^n$) by means of q-deformed Verma modules., Comment: 21 pages, LaTeX, no figures

Let $C$ be an arrangement of affine hyperplanes in a complex affine space $X$, $D$ the ring of algebraic differential operators on $X$. We define a category of quivers associated with $C$. A quiver is a collection of vector spaces, attached to strata of the arrangement, and suitable linear maps between the vector spaces . To a quiver we assign a $D$-module on $X$, called the quiver $D$-module. We describe basic operations for $D$-modules in terms of linear algebra of quivers. We give an explicit construction of a free resolution of a quive $D$-module and use the construction to describe the associated perverse sheaf. As an application, we calculate the cohomology of $X$ with coefficients in the quiver perverse sheaf (under certain assumptions)., Revised version, 92 pages

We construct a family of automorphisms of Mickelsson algebra, satisfying braid group relations. The construction uses ‘Zhelobenko cocycle’ and includes the dynamical Weyl group action as a particular case.