A branch-and-price algorithm for the two-dimensional level strip packing problem

The two-dimensional level strip packing problem (2LSPP) consists in packing rectangular items of given size into a strip of given width divided into levels. Items packed into the same level cannot be put on top of one another and their overall width cannot exceed the width of the strip. The objective is to accommodate all the items while minimizing the overall height of the strip. The problem is -hard and arises from applications in logistics and transportation. We present a set covering formulation of the 2LSPP suitable for a column generation approach, where each column corresponds to a feasible combination of items inserted into the same level. For the exact optimization of the 2LSPP we present a branch-and-price algorithm, in which the pricing problem is a penalized knapsack problem. Computational results are reported for benchmark instances with some hundreds items.     

Coordination chemistry of the cyclo-(P(5)tBu(4))(-) ion: monomeric and oligomeric copper(I), silver(I) and gold(I) complexes

[Na{cyclo-(P(5)tBu(4))}] (1) reacts with [CuCl(PCyp(3))(2)] (Cyp=cyclo-C(5)H(9)) and [CuCl(PPh(3))(3)] (1:1) to give the corresponding copper(I) complexes with a tetra-tert-butylcyclopentaphosphanide ligand, [Cu{cyclo- (P(5)tBu(4))}(PCyp(3))(2)] (2) and [Cu{cyclo-(P(5)tBu(4))}(PPh(3))(2)] (3). The CuCl adduct of 2, [Cu(2)(mu-Cl){cyclo-(P(5)tBu(4))}(PCyp(3))(2)] (4), was obtained from the reaction of 1 with [CuCl(PCyp(3))(2)] (1:2). Compounds 2 and 3 rearrange, even at -27 degrees C, to give [Cu(4){cyclo- (P(4)tBu(3))PtBu}(4)] (5), in which ring contraction of the [cyclo-(P(5)tBu(4))](-) anion has occurred. The reaction of 1 with [AgCl(PCyp(3))](4) or [AgCl(PPh(3))(2)] (1:1) leads to the formation of [Ag(4){cyclo-(P(4)tBu(3))PtBu}(4)] (6). Intermediates, which are most probably mononuclear, "[Ag{cyclo-(P(5)tBu(4))}(PR(3))(2)]" (R=Cyp, Ph) could be detected in the reaction mixtures, but not isolated. Finally, the reaction of 1 with [AuCl(PCyp(3))] (1:1) yielded [Au{cyclo-(P(5)tBu(4))}(PCyp(3))] (7), whereas an inseparable mixture of [Au(3){cyclo-(P(5)tBu(4))}(3)] (8) and [Au(4){cyclo-(P(4)tBu(3))PtBu}(4)] (9) was obtained from the analogous reaction with [AuCl(PPh(3))]. Complexes 3-7 were characterised by (31)P NMR spectroscopy, and X-ray crystal structures were determined for 3-9.     

The synthesis of azadirachtin: a potent insect antifeedant

We describe in full the first synthesis of the potent insect antifeedant azadirachtin through a highly convergent approach. An O-alkylation reaction is used to unite decalin ketone and propargylic mesylate fragments, after which a Claisen rearrangement constructs the central C8-C14 bond in a stereoselective fashion. The allene which results from this sequence then enables a second critical carbon-carbon bond forming event whereby the [3.2.1] bicyclic system, present in the natural product, is generated via a 5-exo-radical cyclisation process. Finally, using knowledge gained through our early studies into the reactivity of the natural product, a series of carefully designed steps completes the synthesis of this challenging molecule.     

Organocatalytic asymmetric synthesis of alpha,alpha-disubstituted alpha-amino acids and derivatives

It is shown that racemic oxazolones are excellent reagents for the synthesis of chiral quaternary amino acids and its derivatives by the diastereo- and enantioselective nucleophilic addition to alpha,beta-unsaturated aldehydes catalyzed by diarylprolinol silyl ethers. The scope of this new organocatalytic reaction is demonstrated for different oxazolones having aromatic and alkyl groups at the reactive carbon atom and different aromatic and aliphatic substituted alpha,beta-unsaturated aldehydes, for which the stereoselective reaction proceeds with good yield, moderate to good to very high diastereoselectivity, and very high enantioselectivity. The potential of the reaction is shown for the synthesis of optically active alpha,alpha-disubstituted alpha-amino acids, alpha-quaternary proline derivatives, amino alcohols, lactams, and tetrahydropyranes. Furthermore, we have calculated by DFT-methods the transition-state structures that account for both the diastereo- and enantioselectivity observed for the addition of oxazolones to the alpha,beta-unsaturated aldehydes. For one class of compounds, the stereoselectivity is controlled by a hydrogen-bonding interaction of the enolate-form of the oxazolone with an ortho-hydroxy-phenyl substituent of the alpha,beta-unsaturated aldehyde, whereas the benzhydryl-protecting group in the oxazolone determines the diastereo- and enantioselectivity in a more general manner for both aromatic and aliphatic alpha,beta-unsaturated aldehydes.     

Adsorption and reaction of 1-epoxy-3-butene on Pt(111): implications for heterogeneous catalysis of unsaturated oxygenates

High-resolution electron energy loss spectroscopy (HREELS), temperature-programmed desorption (TPD), and density functional theory (DFT) calculations were used to study the adsorption and reaction of 1-epoxy-3-butene (EpB) on Pt(111). These investigations were conducted to help elucidate mechanisms for improving olefin hydrogenation selectivity in reactions of unsaturated oxygenates. EpB dosed to Pt(111) at 91 K adsorbs molecularly on the surface through the vinyl group with apparent rehybridization to a di-sigma-bound state. By 233 K, however, EpB undergoes epoxide ring opening to form an aldehyde intermediate, which further decomposes upon heating to yield gas phase products CO, H2, and propylene. Comparison of the HREELS and TPD data to experiments performed with 2-butenal (crotonaldehyde) shows that EpB and 2-butenal decompose through related pathways. However, the EpB-derived aldehyde intermediate clearly has a unique structure, features of which have been elucidated by DFT calculations. In conjunction with previous surface science studies of EpB chemistry, these results can help explain selectivity trends for reactions of EpB on Pt catalysts and bimetallic PtAg catalysts, with indications that the enhanced olefin hydrogenation selectivity of PtAg catalysts likely originates from a bifunctional effect.     

Mechanistic studies of the triggered release of liposomal contents by matrix metalloproteinase-9

Matrix metalloproteinases (MMPs) constitute a class of extracellular-matrix-degrading enzymes overexpressed in many cancers and contribute to the metastatic ability of the cancer cells. We have recently demonstrated that liposomal contents can be released when triggered by the enzyme MMP-9. Herein, we report the results of our mechanistic studies of the MMP-9-triggered release of liposomal contents. We synthesized peptides containing the cleavage site for MMP-9 and conjugated them with fatty acids to prepare the corresponding lipopeptides. By employing circular dichroism (CD) spectroscopy, we demonstrated that the lipopeptides, when incorporated into liposomes, are demixed in the lipid bilayers and generate triple-helical structures. MMP-9 cleaves the triple-helical peptides, leading to the release of the liposomal contents. Other MMPs, which cannot hydrolyze triple-helical peptides, fail to release the contents from the liposomes. We also observed that the rate and extent of release of the liposomal contents depend on the mismatch between the acyl chains of the synthesized lipopeptide and phospholipid components of the liposomes. CD spectroscopic studies imply that the observed differences in the release reflect the ability of the liposomal membrane to anneal the defects following the enzymatic cleavage of the liposome-incorporated lipopeptides.     

Oligonucleotide Analogues with Integrated Bases and Backbone

The thiomethylene‐linked U*[s]U⁽*⁾ dimers 9 – 14 were synthesized by substitution of the 6‐[(mesyloxy)methyl]uridine 6 by the thiolate derived from the uridine‐5′‐thioacetates 7 and 8 followed by O‐deprotection. Similarly, the thiomethylene‐linked A*[s]A⁽*⁾ dimers 9 – 14 were obtained from the 8‐(bromomethyl)adenosine 15 and the adenosine‐5′‐thioacetates 16 and 17 . The concentration dependence of both H? N(3) of the U*[s]U⁽*⁾ dimers 9 – 14 evidences the formation of linear and cyclic duplexes, and of linear higher associates, C(8 or 6)CH₂OH and/or C(5′/II)OH groups favouring the formation of cyclic duplexes. The concentration dependence of the chemical shift for both H₂N? C(6) of the A*[s]A⁽*⁾ dimers 18 – 23 evidences the formation of mainly linear associates. The heteroassociation of U*[s]U⁽*⁾ to A*[s]A⁽*⁾ dimers is stronger than the homoassociation of U*[s]U⁽*⁾ dimers, as evidenced by diluting equimolar mixtures of 11 / 20 and 13 / 22 . A 1 : 1 stoichiometry of the heteroassociation is evidenced by a Job's plot for 11 / 20 , and by mole ratio plots for 9 / 18, 10 / 19, 12 / 21, 13 / 22 , and 14 / 23 .     

Oligonucleotide Analogues with Integrated Bases and Backbones. Part 19.

The A*[s]U⁽*⁾ dinucleosides 1 and 2 form thermoreversible gels in organic solvents. The basis of the gelation is the formation of linear aggregates by base pairing following desolvation of the nucleobases. This is evidenced by the absence of gel formation by the C(6)‐deaminated analogue 3 of 1 , the correlation of gelation with the anti‐conformation, as preferred for 1 , and the temperature‐, concentration‐, and time‐dependent CD spectra. The gels were also characterized by the minimum gelation concentration, the gel–sol transition (melting) temperature, and rheological properties.