An interval branch and bound method for global Robust optimization

In this paper, we design a Branch and Bound algorithm based on interval arithmetic to address nonconvex robust optimization problems. This algorithm provides the exact global solution of such difficult problems arising in many real life applications. A code was developed in MatLab and was used to solve some robust nonconvex problems with few variables. This first numerical study shows the interest of this approach providing the global solution of such difficult robust nonconvex optimization problems.

     

Silver(I) Complexes of Two Flexible Bis-phospholane Ligands: Metallamacrocycles,Polymeric Chains,and Metallacryptands

In a 2:2 reaction with silver(I) chloride or bromide, 1,5-bis(1-phospholano)pentane ( 1a ) afforded frame-like macrocyclic structures, with intra- ( 2 , Cl) or intermolecular ( 3 , Br) halido bridges. In contrast, 1,7-bis(1-phospholano)heptane ( 1b ) formed coordination polymers 4a (Cl) and 4b (Br) with bridging bis-phospholane and halido ligands. A unique paddle wheel-type metallacryptand structure 5 was obtained from 1a and silver(I) bromide in a 2:3 reaction (M:L). All complexes were fully characterized by NMR, IR spectroscopy, mass spectrometry, and X-ray crystallography.     

Dynamics of Bacteriorhodopsin in the Dark-Adapted State from Solution Nuclear Magnetic Resonance Spectroscopy

To achieve efficient proton pumping in the light-driven proton pump bacteriorhodopsin (bR), the protein must be tightly coupled to the retinal to rapidly convert retinal isomerization into protein structural rearrangements. Methyl group dynamics of bR embedded in lipid nanodiscs were determined in the dark-adapted state, and were found to be mostly well ordered at the cytosolic side. Methyl groups in the M145A mutant of bR, which displays only 10 % residual proton pumping activity, are less well ordered, suggesting a link between side-chain dynamics on the cytosolic side of the bR cavity and proton pumping activity. In addition, slow conformational exchange, attributed to low frequency motions of aromatic rings, was indirectly observed for residues on the extracellular side of the bR cavity. This may be related to reorganization of the water network. These observations provide a detailed picture of previously undescribed equilibrium dynamics on different time scales for ground-state bR.     

Vinylic MIDA Boronates: New Building Blocks for the Synthesis of Aza‐Heterocycles

A two‐step synthesis of structurally diverse pyrrole‐containing bicyclic systems is reported. ortho‐Nitro‐haloarenes coupled with vinylic N‐methyliminodiacetic acid (MIDA) boronates generate ortho‐vinyl‐nitroarenes, which undergo a “metal‐free” nitrene insertion, resulting in a new pyrrole ring. This novel synthetic approach has a wide substrate tolerance and it is applicable in the preparation of more complex “drug‐like” molecules. Interestingly, an ortho‐nitro‐allylarene derivative furnished a cyclic β‐aminophosphonate motif.     

Iodine(III)‐Catalyzed Rearrangements of Imides: A Versatile Route to α,α‐Dialkylated α‐Hydroxy Carboxylamides

A tertiary hydroxy group α to a carboxyl moiety comprises a key structural motif in many bioactive substances. With the herein presented metal‐free rearrangement of imides triggered by hypervalent λ³‐iodane, an easy and selective way to gain access to such a compound class, namely α,α‐disubstituted‐α‐hydroxy carboxylamides, was established. Their additional methylene bromide side chain constitutes a useful handle for rapid diversification, as demonstrated by a series of further functionalizations. Moreover, the in situ formation of an iodine(III) species under the reaction conditions was proven. Our findings clearly corroborate that hypervalent λ³‐benziodoxolones are involved in these organocatalytic reactions.