Model theory of operator algebras II: model theory

We introduce a version of logic for metric structures suitable for applications to C*-algebras and tracial von Neumann algebras. We also prove a purely model-theoretic result to the effect that the theory of a separable metric structure is stable if and only if all of its ultrapowers associated with nonprincipal ultrafilters on ? are isomorphic even when the Continuum Hypothesis fails.     

Analysis of the cryptophycin P450 epoxidase reveals substrate tolerance and cooperativity

Cryptophycins are potent anticancer agents isolated from Nostoc sp. ATCC 53789 and Nostoc sp. GSV 224. The most potent natural cryptophycin analogues retain a beta-epoxide at the C2'-C3' position of the molecule. A P450 epoxidase encoded by c rpE recently identified from the cryptophycin gene cluster was shown to install this key functional group into cryptophycin-4 (Cr-4) to produce cryptophycin-2 (Cr-2) in a regio- and stereospecific manner. Here we report a detailed characterization of the CrpE epoxidase using an engineered maltose binding protein (MBP)-CrpE fusion. The substrate tolerance of the CrpE polypeptide was investigated with a series of structurally related cryptophycin analogues generated by chemoenzymatic synthesis. The enzyme specifically installed a beta-epoxide between C2' and C3' of cyclic cryptophycin analogues. The kcat/Km values of the enzyme were determined to provide further insights into the P450 epoxidase catalytic efficiency affected by substrate structural variation. Finally, binding analysis revealed cooperativity of MBP-CrpE toward natural and unnatural desepoxy cryptophycin substrates.     

Molecular Dynamics Simulations Guide Chimeragenesis and Engineered Control of Chemoselectivity in Diketopiperazine Dimerases

In the biosynthesis of the tryptophan-linked dimeric diketopiperazines (DKPs), cytochromes P450 selectively couple DKP monomers to generate a variety of intricate and isomeric frameworks. To determine the molecular basis for selectivity of these biocatalysts we obtained a high-resolution crystal structure of selective Csp²−N bond forming dimerase, AspB. Overlay of the AspB structure onto C−C and C−N bond forming homolog NzeB revealed no significant structural variance to explain their divergent chemoselectivities. Molecular dynamics (MD) simulations identified a region of NzeB with increased conformational flexibility relative to AspB, and interchange of this region along with a single active site mutation led to a variant that catalyzes exclusive C−N bond formation. MD simulations also suggest that intermolecular C−C or C−N bond formation results from a change in mechanism, supported experimentally through use of a substrate mimic.     

Improved bounds for the randomized decision tree Complexity of recursive majority

We consider the randomized decision tree complexity of the recursive 3‐majority function. We prove a lower bound of for the two‐sided‐error randomized decision tree complexity of evaluating height h formulae with error . This improves the lower bound of given by Jayram, Kumar, and Sivakumar (STOC'03), and the one of given by Leonardos (ICALP'13). Second, we improve the upper bound by giving a new zero‐error randomized decision tree algorithm that has complexity at most . The previous best known algorithm achieved complexity . The new lower bound follows from a better analysis of the base case of the recursion of Jayram et al. The new algorithm uses a novel “interleaving” of two recursive algorithms. © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 48, 612–638, 2016     

Metabolic coupling of dehydration and decarboxylation in the curacin A pathway: functional identification of a mechanistically diverse enzyme pair

This study describes the functional identification of a pair of mechanistically diverse enzymes that catalyze the successive dehydration (CurE ECH1) and decarboxylation (CurF ECH2) of (S)-HMG-ACP to generate a 3-methylcrotonyl-ACP intermediate, the presumed precursor of the cyclopropyl ring in curacin A. The reactions catalyzed by ECH1 and ECH2 are found in a broad cross-section of microbial natural product gene clusters and participate in the introduction of carbon chain branch points and functional group diversity as key steps in the HMG-CoA synthase mediated addition of C-2 from acetate to the beta-carbonyl group of polyketide chains.     

Total synthesis of narbonolide and biotransformation to pikromycin

An improved total synthesis of narbonolide and its biotransformation to pikromycin is reported. This total synthesis utilized an intramolecular Nozaki-Hiyama-Kishi coupling that significantly improved macrocyclization yields (90-96%) and allowed for differentiation of the C3- and C5-oxidation states. A pikAI deletion mutant of Streptomyces venezuelae was used to biotransform synthetic narbonolide to pikromycin by glycosylation and oxidation in vivo. This integration of synthetic chemistry and engineered biotransformations holds great promise for the synthesis of novel macrolide analogues of biological interest.