Allyl-indium(III) and -bismuth(III) dihalides, generated by transmetallation of 5-benzyloxy-4-methylpent-2-enyl(tributyl)stannane 1, react with aldehydes with useful levels of 1,5-stereocontrol, a 93:7 ratio of 1,5-epimers in favour of the 1,5-anti-(E)-stereoisomers 7 and 11 typically being obtained using bismuth(III) iodide. The 4-benzyloxypent-2-enylstannane 4 similarly gives the 1,5-syn-(E)-hex-3-enols 13 also with ca. 93:7, stereoselectivity.

Bioactive metabolites have wide-ranging biological activities and are a potential source of future research and therapeutic tools. Here, we use nanovibrational stimulation to induce osteogenic differentiation of mesenchymal stem cells, in the absence of off-target, nonosteogenic differentiation. We show that this differentiation method, which does not rely on the addition of exogenous growth factors to culture media, provides an artifact-free approach to identifying bioactive metabolites that specifically and potently induce osteogenesis. We first identify a highly specific metabolite, cholesterol sulfate, an endogenous steroid. Next, a screen of other small molecules with a similar steroid scaffold identified fludrocortisone acetate with both specific and highly potent osteogenic-inducing activity. Further, we implicate cytoskeletal contractility as a measure of osteogenic potency and cell stiffness as a measure of specificity. These findings demonstrate that physical principles can be used to identify bioactive metabolites and then enable optimization of metabolite potency can be optimized by examining structure-function relationships.

Reactions of 5-benzyloxy-4-methylpent-2-enyl(tributyl)stannane with aldehydes promoted by bismuth(III) iodide were usefully stereoselective in favour of the (E)-1,5-anti-6-benzyloxy-5-methylalk-3-en-1-ols. Similar stereoselectivity was observed for reactions of analogous 5-benzyloxy-4-methylpent-2-enyl bromides with aldehydes when promoted by a low valency bismuth species prepared by reduction of bismuth(III) triiodide with powdered zinc so providing a "tin-free" procedure. The analogous reactions of 4-benzyloxypent-2-enyl(tributyl)stannane with aldehydes promoted by bismuth(III) iodide were also stereoselective but gave lower yields. Attempted 1,6-stereocontrol using these reactions resulted in only modest stereoselectivities. Aspects of the chemistry of the products were studied in particular their stereoselective conversion into aliphatic compounds with methyl bearing stereogenic centres at 1,5,9,13- and 1,3,5-positions along the aliphatic chain. Mechanistically, allylic organobismuth species may be involved in both sets of reactions but this was not confirmed although the similar stereoselectivities observed for both the bismuth(III) iodide mediated reactions of the pent-2-enylstannanes and the low-valency bismuth promoted reactions of the pent-2-enyl bromides are consistent with participation of similar intermediates.

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We examine powers of Hamiltonian paths and cycles as well as Hamiltonian (power) completion problems in several highly structured graph classes. For threshold graphs we give efficient algorithms as well as sufficient and minimax toughness like conditions. For arborescent comparability graphs we have similar results but also show that for one type of completion problem an 'obvious' minimax condition fails. For cographs we give examples showing that toughness and other 'obvious' necessary conditions are not sufficient. For threshold graphs we give additional necessary and sufficient conditions in terms of vertex degrees as well as a minimax formula for the length of a longest cycle power.