Synthesis,separation and N.M.R. spectra of three double bond isomers of leukotriene a methyl ester

The synthesis and h.p.l.c. separation of three double bond isomers of leukotriene A methyl ester is described, their stereochemistry being assigned by ¹H N.M.R.     

Feasibility conditions for the existence of walk-regular graphs

A graph X is walk-regular if the vertex-deleted subgraphs of X all have the same characteristic polynomial. Examples of such graphs are vertex-transitive graphs and distance-regular graphs. We show that the usual feasibility conditions for the existence of a distance-regular graph with a given intersection array can be extended so that they apply to walk-regular graphs. Despite the greater generality, our proofs are more elementary than those usually given for distance-regular graphs. An application to the computation of vertex-transitive graphs is described.     

Polynomials with PSL(2, 7) as Galois group

We describe a technique for determining the set-transitivity of the Galois group of a polynomial over the rationals. As an application we give a short proof that the polynomial P₇(x) = x⁷ ? 154x + 99 has the simple group PSL(2, 7) of order 168 as its Galois group over the rationals. A similar method is used to prove that the associated splitting field is not that of the polynomial x⁷ ? 7x + 3 given by Trinks [9].     

Switching Reconstruction of Digraphs

Switching about a vertex in a digraph means to reverse the direction of every edge incident with that vertex. Bondy and Mercier introduced the problem of whether a digraph can be reconstructed up to isomorphism from the multiset of isomorphism types of digraphs obtained by switching about each vertex. Since the largest known nonreconstructible oriented graphs have eight vertices, it is natural to ask whether there are any larger nonreconstructible graphs. In this article, we continue the investigation of this question. We find that there are exactly 44 nonreconstructible oriented graphs whose underlying undirected graphs have maximum degree at most 2. We also determine the full set of switching‐stable oriented graphs, which are those graphs for which all switchings return a digraph isomorphic to the original.     

On the Chromatic Number of Subsets of the Euclidean Plane

The chromatic number of a subset of the real plane is the smallest number of colors assigned to the elements of that set such that no two points at distance 1 receive the same color. It is known that the chromatic number of the plane is at least 4 and at most 7. In this note, we determine the bounds on the chromatic number for several classes of subsets of the plane such as extensions of the rational plane, sets in convex position, infinite strips, and parallel lines.     

Cellular consequences of copper complexes used to catalyze bioorthogonal click reactions

Copper toxicity is a critical issue in the development of copper-based catalysts for copper(I)-catalyzed azide-alkyne cycloaddition (CuAAC) reactions for applications in living systems. The effects and related toxicity of copper on mammalian cells are dependent on the ligand environment. Copper complexes can be highly toxic, can induce changes in cellular metabolism, and can be rapidly taken up by cells, all of which can affect their ability to function as catalysts for CuAAC in living systems. Herein, we have evaluated the effects of a number of copper complexes that are typically used to catalyze CuAAC reactions on four human cell lines by measuring mitochondrial activity based on the metabolism of 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) to study toxicity, inductively coupled plasma mass spectrometry to study cellular uptake, and coherent anti-Stokes Raman scattering (CARS) microscopy to study effects on lipid metabolism. We find that ligand environment around copper influences all three parameters. Interestingly, for the Cu(II)-bis-L-histidine complex (Cu(his)(2)), cellular uptake and metabolic changes are observed with no toxicity after 72 h at micromolar concentrations. Furthermore, we show that under conditions where other copper complexes kill human hepatoma cells, Cu(I)-L-histidine is an effective catalyst for CuAAC labeling of live cells following metabolic incorporation of an alkyne-labeled sugar (Ac(4)ManNAl) into glycosylated proteins expressed on the cell surface. This result suggests that Cu(his)(2) or derivatives thereof have potential for in vivo applications where toxicity as well as catalytic activity are critical factors for successful bioconjugation reactions.     

Photocatalytic α‐Tertiary Amine Synthesis via C−H Alkylation of Unmasked Primary Amines

A practical, catalytic entry to α,α,α‐trisubstituted (α‐tertiary) primary amines by C?H functionalisation has long been recognised as a critical gap in the synthetic toolbox. We report a simple and scalable solution to this problem that does not require any in situ protection of the amino group and proceeds with 100 % atom‐economy. Our strategy, which uses an organic photocatalyst in combination with azide ion as a hydrogen atom transfer (HAT) catalyst, provides a direct synthesis of α‐tertiary amines, or their corresponding γ‐lactams. We anticipate that this methodology will inspire new retrosynthetic disconnections for substituted amine derivatives in organic synthesis, and particularly for challenging α‐tertiary primary amines.