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

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