Weak splittings of quotients of Drinfeld and Heisenberg doubles

We investigate the fine structure of the simplectic foliations of Poisson homogeneous spaces. Two general results are proved for weak splittings of surjective Poisson submersions from Heisenberg and Drinfeld doubles. The implications of these results are that the torus orbits of symplectic leaves of the quotients can be explicitly realized as Poisson-Dirac submanifolds of the torus orbits of the doubles. The results have a wide range of applications to many families of real and complex Poisson structures on flag varieties. Their torus orbits of leaves recover important families of varieties such as the open Richardson varieties.Comment: 20 pages, AMS Late

Quantum cohomology via vicious and osculating walkers

We relate the counting of rational curves intersecting Schubert varieties of the Grassmannian to the counting of certain non-intersecting lattice paths on the cylinder, so-called vicious and osculating walkers. These lattice paths form exactly solvable statistical mechanics models and are obtained from solutions to the Yang–Baxter equation. The eigenvectors of the transfer matrices of these models yield the idempotents of the Verlinde algebra of the gauged u^(n)k -WZNW model. The latter is known to be closely related to the small quantum cohomology ring of the Grassmannian. We establish further that the partition functions of the vicious and osculating walker model are given in terms of Postnikov’s toric Schur functions and can be interpreted as generating functions for Gromov–Witten invariants. We reveal an underlying quantum group structure in terms of Yang–Baxter algebras and use it to give a generating formula for toric Schur functions in terms of divided difference operators which appear in known representations of the nil-Hecke algebra

A Symmetrical UV to Vis/NIR Benzothiadiazole Redox Switch

Reversibly switching the light absorption of organic molecules by redox processes is of interest for applications in sensors, light harvesting, smart materials, and medical diagnostics. This work presents a symmetrical benzothiadiazole (BTD) derivative with a high fluorescence quantum yield in solution and in the crystalline state and shows by spectroelectrochemical analysis that reversible switching of UV absorption in the neutral state, to broadband Vis/NIR absorption in the 1st oxidized state, to sharp band Vis absorption in the 2nd oxidized state, is possible. For the one‐electron oxidized species, formation of a delocalized radical is confirmed by electron paramagnetic resonance spectroelectrochemistry. Furthermore, our results reveal an increasing quinoidal distortion upon the 1st and 2nd oxidation, which can be used as the leitmotif for the development of BTD based redox switches

Between Aromatic and Quinoid Structure: A Symmetrical UV to Vis/NIR Benzothiadiazole Redox Switch

Reversibly switching the light absorption of organic molecules by redox processes is of interest for applications in sensors, light harvesting, smart materials, and medical diagnostics. This work presents a symmetrical benzothiadiazole (BTD) derivative with a high fluorescence quantum yield in solution and in the crystalline state and shows by spectroelectrochemical analysis that reversible switching of UV absorption in the neutral state, to broadband Vis/NIR absorption in the 1st oxidized state, to sharp band Vis absorption in the 2nd oxidized state, is possible. For the one-electron oxidized species, formation of a delocalized radical is confirmed by electron paramagnetic resonance spectroelectrochemistry. Furthermore, our results reveal an increasing quinoidal distortion upon the 1st and 2nd oxidation, which can be used as the leitmotif for the development of BTD based redox switches. © 2020 The Authors. Published by Wiley-VCH Gmb

Mask formulas for cograssmannian Kazhdan-Lusztig polynomials

We give two contructions of sets of masks on cograssmannian permutations that can be used in Deodhar's formula for Kazhdan-Lusztig basis elements of the Iwahori-Hecke algebra. The constructions are respectively based on a formula of Lascoux-Schutzenberger and its geometric interpretation by Zelevinsky. The first construction relies on a basis of the Hecke algebra constructed from principal lower order ideals in Bruhat order and a translation of this basis into sets of masks. The second construction relies on an interpretation of masks as cells of the Bott-Samelson resolution. These constructions give distinct answers to a question of Deodhar.Comment: 43 page

Oxidative protein folding in bacteria

Ten years ago it was thought that disulphide bond formation in prokaryotes occurred spontaneously. Now two pathways involved in disulphide bond formation have been well characterized, the oxidative pathway, which is responsible for the formation of disulphides, and the isomerization pathway, which shuffles incorrectly formed disulphides. Disulphide bonds are donated directly to unfolded polypeptides by the DsbA protein; DsbA is reoxidized by DsbB. DsbB generates disulphides de novo from oxidized quinones. These quinones are reoxidized by the electron transport chain, showing that disulphide bond formation is actually driven by electron transport. Disulphide isomerization requires that incorrect disulphides be attacked using a reduced catalyst, followed by the redonation of the disulphide, allowing alternative disulphide pairing. Two isomerases exist in Escherichia coli , DsbC and DsbG. The membrane protein DsbD maintains these disulphide isomerases in their reduced and thereby active form. DsbD is kept reduced by cytosolic thioredoxin in an NADPH-dependent reaction.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75150/1/j.1365-2958.2002.02851.x.pd

Expert system for predicting reaction conditions: The Michael reaction case

© 2015 American Chemical Society. A generic chemical transformation may often be achieved under various synthetic conditions. However, for any specific reagents, only one or a few among the reported synthetic protocols may be successful. For example, Michael β-addition reactions may proceed under different choices of solvent (e.g., hydrophobic, aprotic polar, protic) and catalyst (e.g., Brønsted acid, Lewis acid, Lewis base, etc.). Chemoinformatics methods could be efficiently used to establish a relationship between the reagent structures and the required reaction conditions, which would allow synthetic chemists to waste less time and resources in trying out various protocols in search for the appropriate one. In order to address this problem, a number of 2-classes classification models have been built on a set of 198 Michael reactions retrieved from literature. Trained models discriminate between processes that are compatible and respectively processes not feasible under a specific reaction condition option (feasible or not with a Lewis acid catalyst, feasible or not in hydrophobic solvent, etc.). Eight distinct models were built to decide the compatibility of a Michael addition process with each considered reaction condition option, while a ninth model was aimed to predict whether the assumed Michael addition is feasible at all. Different machine-learning methods (Support Vector Machine, Naive Bayes, and Random Forest) in combination with different types of descriptors (ISIDA fragments issued from Condensed Graphs of Reactions, MOLMAP, Electronic Effect Descriptors, and Chemistry Development Kit computed descriptors) have been used. Models have good predictive performance in 3-fold cross-validation done three times: balanced accuracy varies from 0.7 to 1. Developed models are available for the users at http://infochim.u-strasbg.fr/webserv/VSEngine.html. Eventually, these were challenged to predict feasibility conditions for ∼50 novel Michael reactions from the eNovalys database (originally from patent literature)

Disruption of reducing pathways is not essential for efficient disulfide bond formation in the cytoplasm of E. coli

<p>Abstract</p> <p>Background</p> <p>The formation of native disulfide bonds is a complex and essential post-translational modification for many proteins. The large scale production of these proteins can be difficult and depends on targeting the protein to a compartment in which disulfide bond formation naturally occurs, usually the endoplasmic reticulum of eukaryotes or the periplasm of prokaryotes. It is currently thought to be impossible to produce large amounts of disulfide bond containing protein in the cytoplasm of wild-type bacteria such as <it>E. coli </it>due to the presence of multiple pathways for their reduction.</p> <p>Results</p> <p>Here we show that the introduction of Erv1p, a sulfhydryl oxidase and FAD-dependent catalyst of disulfide bond formation found in the inter membrane space of mitochondria, allows the efficient formation of native disulfide bonds in heterologously expressed proteins in the cytoplasm of <it>E. coli </it>even without the disruption of genes involved in disulfide bond reduction, for example <it>trxB </it>and/or <it>gor</it>. Indeed yields of active disulfide bonded proteins were higher in BL21 (DE3) pLysSRARE, an <it>E. coli </it>strain with the reducing pathways intact, than in the commercial Δ<it>gor </it>Δ<it>trxB </it>strain rosetta-gami upon co-expression of Erv1p.</p> <p>Conclusions</p> <p>Our results refute the current paradigm in the field that disruption of at least one of the reducing pathways is essential for the efficient production of disulfide bond containing proteins in the cytoplasm of <it>E. coli </it>and open up new possibilities for the use of <it>E. coli </it>as a microbial cell factory.</p

Generalizing Tanisaki's ideal via ideals of truncated symmetric functions

We define a family of ideals $I_h$ in the polynomial ring $\mathbb{Z}[x_1,...,x_n]$ that are parametrized by Hessenberg functions $h$ (equivalently Dyck paths or ample partitions). The ideals $I_h$ generalize algebraically a family of ideals called the Tanisaki ideal, which is used in a geometric construction of permutation representations called Springer theory. To define $I_h$, we use polynomials in a proper subset of the variables ${x_1,...,x_n}$ that are symmetric under the corresponding permutation subgroup. We call these polynomials {\em truncated symmetric functions} and show combinatorial identities relating different kinds of truncated symmetric polynomials. We then prove several key properties of $I_h$, including that if $h>h'$ in the natural partial order on Dyck paths then $I_{h} \subset I_{h'}$, and explicitly construct a Gr\"{o}bner basis for $I_h$. We use a second family of ideals $J_h$ for which some of the claims are easier to see, and prove that $I_h = J_h$. The ideals $J_h$ arise in work of Ding, Develin-Martin-Reiner, and Gasharov-Reiner on a family of Schubert varieties called partition varieties. Using earlier work of the first author, the current manuscript proves that the ideals $I_h = J_h$ generalize the Tanisaki ideals both algebraically and geometrically, from Springer varieties to a family of nilpotent Hessenberg varieties.Comment: v1 had 27 pages. v2 is 29 pages and adds Appendix B, where we include a recent proof by Federico Galetto of a conjecture given in the previous version. We also add some connections between our work and earlier results of Ding, Gasharov-Reiner, and Develin-Martin-Reiner. v3 corrects a typo in Valibouze's citation in the bibliography. To appear in Journal of Algebraic Combinatoric