Symmetric Grothendieck polynomials, skew Cauchy identities, and dual filtered Young graphs

Symmetric Grothendieck polynomials are analogues of Schur polynomials in the K-theory of Grassmannians. We build dual families of symmetric Grothendieck polynomials using Schur operators. With this approach we prove skew Cauchy identity and then derive various applications: skew Pieri rules, dual filtrations of Young's lattice, generating series and enumerative identities. We also give a new explanation of the finite expansion property for products of Grothendieck polynomials

Electoral systems and forms of abstention

Stereoselective biocatalysis by crotonase superfamily enzymes is exemplified by use of engineered 5-carboxymethylproline synthases (CMPSs) for preparation of functionalized 5-carboxymethylproline (5-CMP) derivatives methylated at two positions (i.e., C2/C6, C3/C6, and C5/C6), including products with a quaternary center, from appropriately substituted-amino acid aldehydes and C-2 epimeric methylmalonyl-CoA. The enzymatically produced disubstituted 5-CMPs were converted by carbapenam synthetase into methylated bicyclic β-lactams, which manifestly improved hydrolytic stability compared to the unsubstituted carbapenams. The results highlight the use of modified carbapenem biosynthesis enzymes for production of carbapenams with improved properties

Overview of glutathione-dependent formaldehyde metabolism.

<p>(A) Summary scheme of glutathione-dependent formaldehyde metabolism. Formaldehyde (HCHO) reacts with glutathione (GSH) via its nucleophilic thiol group to form <i>S</i>-hydroxymethylglutathione (HMG), which is a substrate of glutathione-dependent alcohol dehydrogenase (ADH, ADH5 in humans). The product, <i>S</i>-formylglutathione, is then further metabolised by <i>S</i>-formylglutathione hydrolase to give formate and GSH. The reaction of HCHO and GSH, i.e. the first step in GSH-dependent metabolism, occurs spontaneously in aqueous solution; however, the reaction might also be catalysed by GFA (and homologues in other organisms, e.g. CENPV in humans[<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0145085#pone.0145085.ref013" target="_blank">13</a>]). There is also evidence, at least <i>in vitro</i>, that GSH can react with HCHO to form cyclised adducts[<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0145085#pone.0145085.ref010" target="_blank">10</a>–<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0145085#pone.0145085.ref012" target="_blank">12</a>]. (B) Views of X-ray crystal structures of GFA from <i>Paracoccus denitrificans</i> (PDB IDs: 1X6M and 1XA8[<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0145085#pone.0145085.ref014" target="_blank">14</a>]). The GFA domain contains two zinc binding sites; one zinc ion is coordinated by four cysteinyl thiols (C31, C33, C99 and C102) in a tetrahedral geometry, whereas the other zinc ion is coordinated by three cysteinyl thiols (C52, C54 and C57) in a trigonal planar geometry. Crystallographic studies have proposed that GSH binding induces translocation of the second zinc ion (circles)[<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0145085#pone.0145085.ref014" target="_blank">14</a>].</p

GFA is a GSH-binding protein that induces an increase in EXSY correlation intensities between GSH and HMG, but does not catalyse HMG formation / fragmentation.

<p>(A) 2D EXSY spectra of equilibrium mixtures of GSH (initial concentration 15 mM) and HMG in the absence (left) and presence (right) of GFA (20 μM). Mixing time (τ_m) = 400 ms. EXSY-correlation intensities between GSH and HMG are increased in the presence of GFA. (B) 1D EXSY spectra of equilibrium mixtures of GSH (initial concentration 15 mM) and HMG in the presence of GFA (20 μM) conducted at different mixing times (τ_m = 32–300 ms). Irradiation (inversion) of a β-cysteinyl resonance of HMG (δ_H 2.95 ppm) induced an exchange correlation at δ_H 2.87 ppm, corresponding to the β-cysteinyl resonance of GSH, which increased in intensity at longer mixing times. (C) Graph showing the intensity of the GSH cross-peak relative to the inverted HMG resonance in the absence and presence of GFA at different mixing times, using either NOESY or ROESY pulse sequences. τ_m = 4–400 ms. (D) Bar graph showing the intensity of the GSH 1D EXSY-correlation relative to the irradiated HMG resonance in the absence (blue) and presence (green) of GFA (τ_m = 80 ms). The build-up rates of the 1D EXSY analyses (note: a τ_m of 80 ms is within the linear range of the EXSY build-up curves, Fig 2C) correlate with the rates of GSH/HMG exchange at equilibrium. Therefore, the observed increase in correlation intensity in the presence of GFA implies an increase in GSH/HMG inter-conversion rate. (E) Non-denaturing MS analyses of GSH binding to GFA. Two new peaks corresponding to the masses of monomeric GFA (with two zinc ions in complex) bound to one and two GSH molecules respectively were observed upon incubation with GSH (4 equivalents, right). (F) Binding curve of GSH binding to GFA obtained using waterLOGSY. Selective irradiation of the solvent H₂O ¹H resonance results in magnetisation transfer to GSH, resulting in the emergence of GSH ¹H resonances with opposite sign to the irradiated H₂O resonance. The (negative) intensities of the GSH resonances are linearly dependent on the GSH concentration (blue). Addition of GFA results in a slower net tumbling rate for GSH in solution due to binding with GFA. The slower tumbling rate leads to ‘(more) positive’ GSH resonance intensities as a function of the extent of ligand binding (green). Subtraction of the intensities in the absence (blue) and presence (green) of GFA gives a normalised binding curve (orange, K_D value of roughly 500 μM assuming binding of one GSH molecule per GFA subunit). The experiments were carried out at 280 K. τ_m = 1 s. (G) Graph showing production of HMG from mixtures of GSH (13.3 mM) and HCHO (13.3 mM) in the absence (blue) and presence (green) of GFA (16 μM) in BisTris buffer pH 6.0. GFA does not affect the initial HMG formation rate.</p

Crotonase Catalysis Enables Flexible Production of Functionalized Prolines and Carbapenams

The biocatalytic versatility of wildtype and engineered carboxymethylproline synthases (CMPSs) is demonstrated by the preparation of functionalized 5-carboxymethylproline derivatives methylated at C-2, C-3, C-4, or C-5 of the proline ring from appropriately substituted amino acid aldehydes and malonyl-coenzyme A. Notably, compounds with a quaternary center (at C-2 or C-5) were prepared in a stereoselective fashion by engineered CMPSs. The substituted-5-carboxymethyl-prolines were converted into the corresponding bicyclic β-lactams using a carbapenam synthetase. The results demonstrate the utility of the crotonase superfamily enzymes for stereoselective biocatalysis, the amenability of carbapenem biosynthesis pathways to engineering for the production of new bicyclic β-lactam derivatives, and the potential of engineered biocatalysts for the production of quaternary centers

Crotonase Catalysis Enables Flexible Production of Functionalized Prolines and Carbapenams

The biocatalytic versatility of wildtype and engineered carboxymethylproline synthases (CMPSs) is demonstrated by the preparation of functionalized 5-carboxymethylproline derivatives methylated at C-2, C-3, C-4, or C-5 of the proline ring from appropriately substituted amino acid aldehydes and malonyl-coenzyme A. Notably, compounds with a quaternary center (at C-2 or C-5) were prepared in a stereoselective fashion by engineered CMPSs. The substituted-5-carboxymethyl-prolines were converted into the corresponding bicyclic β-lactams using a carbapenam synthetase. The results demonstrate the utility of the crotonase superfamily enzymes for stereoselective biocatalysis, the amenability of carbapenem biosynthesis pathways to engineering for the production of new bicyclic β-lactam derivatives, and the potential of engineered biocatalysts for the production of quaternary centers