On Poset Boolean Algebras

Let (P,≤) be a partially ordered set. The poset Boolean algebra of P, denoted F(P), is defined as follows: The set of generators of F(P) is {x _p  : p∈P}, and the set of relations is {x _p ⋅x _q =x _p  : p≤q}. We say that a Boolean algebra B is well-generated, if B has a sublattice G such that G generates B and (G,≤ ^B |G) is well-founded. A well-generated algebra is superatomic. THEOREM 1. Let (P,≤) be a partially ordered set. The following are equivalent. (i) P does not contain an infinite set of pairwise incomparable elements, and P does not contain a subset isomorphic to the chain of rational numbers, (ii) F(P) is superatomic, (iii) F(P) is well-generated. The equivalence (i) ⇔ (ii) is due to M. Pouzet. A partially ordered set W is well-ordered, if W does not contain a strictly decreasing infinite sequence, and W does not contain an infinite set of pairwise incomparable elements. THEOREM 2. Let F(P) be a superatomic poset algebra. Then there are a well-ordered set W and a subalgebra B of F(W), such that F(P) is a homomorphic image of B. This is similar but weaker than the fact that every interval algebra of a scattered chain is embeddable in an ordinal algebra. Remember that an interval algebra is a special case of a poset algebra. This revised version was published online in June 2006 with corrections to the Cover Date.     

Post-translational modification of Rhodococcus R312 and Comamonas NI1 nitrile hydratases

Nitrile hydratases (NHases) are industrially significant iron- and cobalt-containing enzymes used in the large-scale synthesis of acrylamide. Previous reports have shown that the active site peptides of NHases are post-translationally modified by oxidation of cysteine residues, and that these modifications are essential for catalysis. We report mass spectrometric evidence of the oxidation states of the active site cysteines in the iron coordination spheres of two iron-containing nitrile hydratases, namely R312 NHase from Rhodococcus rhodochrous strain R312 and NI1 NHase from Comamonas testosteroni. At least one of these cysteines is oxidised to a sulfinic acid (SO(2)H) and there is also evidence suggesting an additional oxidation to a sulfenic acid (SOH). This is the first evidence for the presence of these oxidation states for full-length NHases and for Fe-NHases from different microorganisms. The presence of these covalent modifications was confirmed by performing mass spectrometry on the active site peptide of R312 NHase, under native, reduced and carboxymethylated conditions. We also show the nitrosylation of the iron by mass spectrometry, as well as the release of NO by photoirradiation.     

X-ray and neutron diffraction studies of the hydridotriruthenium cluster complex (μ-H)Ru3(CO)7(μ-As(C6H5)CH2As(C6H5)2) ((C6H5 2AsCH2As(C6H5)·CH2Cl2: an example of dibridged metal-metal bond M(μ-H)(μ-X)M,involving a heavy bridgehead atom

The title compound is (μ-H)Ru₃(CO)₇(μ-As(C₆H₅)CH₂As(C₆H₅)₂)((C₆H₅)₂ AsCH₂As(C₆H₅)₂)·CH₂C1₂. Crystal data: monoclinic,P2₁/n, cell parameters (X-ray)a=12.82(2) Å,b=22.91(2) Å,c=17.83(2) Å, β=99.1(3)°; (neutron)a=12.94(1) Å, β=22.95(2)Å,c=17.93(3)Å,β=99.55(5)°. The structure was solved from X-ray data. FinalR indices areR(F)=0.051,R _w (F)=0.049 (X-ray);R(F)=0.064,R _w (F)=0.048,R(F ²)=0.072,R _w (F²)=0.088 (neutron). The complex is derived from Ru₃(CO)₈(dpam)₂ through reaction with hydrogen. The structure consists of a triangular array of metal atoms involving three metal-metal bonds[Ru(1)?Ru(2)=2.912(7)Å;Ru(1)?Ru(3)=2.829(3) A; Ru(2)?Ru(3)=2.845(6) Å]. The metal-metal edge Ru(1)?Ru(2) is supported by a bridging bis(diphenylarsino)methane ligand which lies in the equatorial plane. Activation of the second dpam ligand has generated the new face-bridging ligand unit μ-As(C₆H₅)CH₂As(C₆H₅)₂. In this unit, the bridgehead As atom spans over the Ru(1)?Ru(2) bond, while the second As atom is only bonded to Ru(3). The metal environment is achieved by CO ligands. The hydride ligand is bridging the Ru(1)?Ru(2) vector [Ru(1)?H=1.791(10) Å; Ru(2)?H=1.818(8) Å]. Geometric features of the dibridged Ru(μ-H)(μ-As)Ru bond are discussed.     

Semi-coherent interfaces without length misfit accommodation in a lamellar Al–Al2Cu eutectic

Abstract

The interfacial structure of a lamellar Al(α)-Al₂Cu(θ) eutectic obtained by directional solidification is investigated using conventional transmission electron microscopy (TEM) and high-resolution TEM. The average lamellar habit plane is close to (2 3 3)α and lie 10° from the atomically densest planes (1 1 1)α//(2 –1 1)θ. Networks of linear contrasted features are observed along the interfaces, the lines being separated each other’s in a wide range of spacings, typically 6–500 nm. These features are identified as interfacial dislocations with 1/2<1 1 0>α Burgers vectors from image contrast analysis. According to previous works, they are associated with ledge-like defects, the heights of which can reach 3 nm. The high-resolution TEM images do not confirm the presence of atomic terraces parallel to the atomically dense plane (1 1 1)α or the habit plane (2 3 3)α. The interface ensures the quasi-continuity of atomically dense planes, which is a configuration corresponding to the plane-matching model. It is suggested that α/θ interfaces can be considered as semi-coherent but in a particular sense since, according to our analysis, the theoretical length misfits between the fcc and bct lattices are too large to explain the presence of some loose dislocation networks. Their general irregular geometry suggests that these dislocation networks behave like non-equilibrated low-angle grain boundaries superposed on the α–θ interfaces.     

Classical photodissociation dynamics with Bohr quantization

The standard classical expression of the state-resolved photodissociation cross section is not consistent with an efficient Bohr quantization of product internal motions. A new and strictly equivalent expression not suffering from this drawback is proposed. This expression opens the way to more realistic classical simulations of direct polyatomic photodissociations in the quantum regime where only a few states are available to the products.     

The diffusion constant of a labeled protein sliding along DNA

Long ago inferred by biochemists, the linear diffusion of proteins along DNA has recently been observed at a single-molecule level using fluorescence microscopy. This imaging technique requires labeling the protein of interest with a fluorophore, usually an organic nanosized dye that is not supposed to impact the dynamics of the protein. Yet individual proteins can also be tracked using much larger labels, like quantum dots or beads. We investigate here the impact of such a large label on the protein diffusion along DNA. Solving a Fokker-Planck equation, we estimate the diffusion constant of a protein-label complex diffusing in a periodic potential that mimics the DNA-protein interaction, the link between the protein and the label being modeled as a Hookean spring. Our results indicate that the diffusion constant can generally be calculated by considering that the motion of the protein in the DNA potential is decoupled from the Brownian motion of the label. Our conclusions are in good agreement with the experimental results we obtained with the restriction enzyme EcoRV, assuming a rotation-coupled diffusion of the enzyme along DNA.     

Donor-Stabilized Silylene/Phosphine-Supported Carbon(0) Center with High Electron Density

An isolable donor-stabilized silavinylidene phosphorane was synthesized. This molecule, which can also be regarded as a new carbon(0) complex featuring a phosphine and a donor-stabilized silylene ligand, presents a central carbon atom with a remarkably high electron density (−1.82). Furthermore, the experimental electron-density study of this compound demonstrates the delocalization of the σ-lone pair at the central carbon atom toward the silicon center, a feature which is remarkably different from electronic situation of other bent-allene-type molecules. This result clearly demonstrates the powerful electron-donating ability of donor-stabilized silylene ligands, as well as their excellent electron-acceptor properties.     

Iron‐Catalyzed Trifluoromethylation of Enamide

Herein the first example of the iron(II)‐catalyzed trifluoromethylation of enamide using mild and simple reaction conditions is reported. The method is cost‐effective and uses the easy‐to‐handle Togni’s reagent as the electrophilic CF₃ source. This transformation is totally regioselective at the C3 position of enamides and exhibits broad substrate scope, good functional group tolerance and thus demonstrates its useful application in a late‐stage fluorination strategy.