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

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

Structural Basis for Type VI Secretion Effector Recognition by a Cognate Immunity Protein

The type VI secretion system (T6SS) has emerged as an important mediator of interbacterial interactions. A T6SS from Pseudomonas aeruginosa targets at least three effector proteins, type VI secretion exported 1–3 (Tse1–3), to recipient Gram-negative cells. The Tse2 protein is a cytoplasmic effector that acts as a potent inhibitor of target cell proliferation, thus providing a pronounced fitness advantage for P. aeruginosa donor cells. P. aeruginosa utilizes a dedicated immunity protein, type VI secretion immunity 2 (Tsi2), to protect against endogenous and intercellularly-transferred Tse2. Here we show that Tse2 delivered by the T6SS efficiently induces quiescence, not death, within recipient cells. We demonstrate that despite direct interaction of Tsi2 and Tse2 in the cytoplasm, Tsi2 is dispensable for targeting the toxin to the secretory apparatus. To gain insights into the molecular basis of Tse2 immunity, we solved the 1.00 Å X-ray crystal structure of Tsi2. The structure shows that Tsi2 assembles as a dimer that does not resemble previously characterized immunity or antitoxin proteins. A genetic screen for Tsi2 mutants deficient in Tse2 interaction revealed an acidic patch distal to the Tsi2 homodimer interface that mediates toxin interaction and immunity. Consistent with this finding, we observed that destabilization of the Tsi2 dimer does not impact Tse2 interaction. The molecular insights into Tsi2 structure and function garnered from this study shed light on the mechanisms of T6 effector secretion, and indicate that the Tse2–Tsi2 effector–immunity pair has features distinguishing it from previously characterized toxin–immunity and toxin–antitoxin systems

Identification of Chromosomal Genes in Yersinia pestis that Influence Type III Secretion and Delivery of Yops into Target Cells

Pathogenic Yersinia species possess a type III secretion system, which is required for the delivery of effector Yop proteins into target cells during infection. Genes encoding the type III secretion machinery, its substrates, and several regulatory proteins all reside on a 70-Kb virulence plasmid. Genes encoded in the chromosome of yersiniae are thought to play important roles in bacterial perception of host environments and in the coordinated activation of the type III secretion pathway. Here, we investigate the contribution of chromosomal genes to the complex regulatory process controlling type III secretion in Yersinia pestis. Using transposon mutagenesis, we identified five chromosomal genes required for expression or secretion of Yops in laboratory media. Four out of the five chromosomal mutants were defective to various extents at injecting Yops into tissue culture cells. Interestingly, we found one mutant that was not able to secrete in vitro but was fully competent for injecting Yops into host cells, suggesting independent mechanisms for activation of the secretion apparatus. When tested in a mouse model of plague disease, three mutants were avirulent, whereas two strains were severely attenuated. Together these results demonstrate the importance of Y. pestis chromosomal genes in the proper function of type III secretion and in the pathogenesis of plague