Toward [18F]-labeled aryltrifluoroborate radiotracers: in vivo positron emission tomography imaging of stable aryltrifluoroborate clearance in mice

The use of a boronic ester as a captor of aqueous [(18)F]-fluoride has been previously suggested as a means of labeling biomolecules in one step for positron emission tomography (PET) imaging. For this approach to be seriously considered, the [(18)F]-labeled trifluoroborate should be humorally stable such that it neither leaches free [(18)F]-fluoride to the bone nor accumulates therein. Herein, we have synthesized a biotinylated boronic ester that is converted to the corresponding trifluoroborate salt in the presence of aqueous [(18)F]-fluoride. In keeping with its in vitro aqueous kinetic stability at pH 7.5, the trifluoroborate appears to clear in vivo quite rapidly to the bladder as the stable trifluoroborate salt with no detectable leaching of free [(18)F]-fluoride to the bone. When this labeled biotin is preincubated with avidin, the pharmacokinetic clearance of the resulting complex is visibly altered. This work validates initial claims that boronic esters are potentially useful as readily labeled precursors to [(18)F]-PET reagents.     

Reversible intramolecular C-C bond formation/breaking and color switching mediated by a N,C-chelate in (2-ph-py)BMes2 and (5-BMes2-2-ph-py)BMes2

A diboron compound with both 3-coordinate boron and 4-coordinate boron centers, (5-BMes2-2-ph-py)BMes2 (1) and its monoboron analogue, (2-ph-py)BMes2 (2) have been synthesized. Both compounds are luminescent but have a high sensitivity toward light. UV and ambient light cause both compounds to isomerize to 1a and 2a, respectively, via the formation of a C-C bond between a mesityl and the phenyl group, accompanied by a drastic color change from yellow or colorless to dark olive green or dark blue. The structures of 1a and 2a were established by 2D NMR experiments and geometry optimization by DFT calculations. Both 1a and 2a can thermally reverse back to 1 and 2 via the breaking of a C-C bond, with the activation barrier being 107 and 110 kJ/mol, respectively. The N,C-chelate ligands in 1 and 2 were found to play a key role in promoting this unusual and reversible photo-thermal isomerization process on a tetrahedral boron center. Reactions with oxygen molecules convert 1a and 2a to 5-BMes2-2-[(2-Mes)-ph]-pyridine (1b) and 2-(2-Mes)-ph-pyridine (2b), respectively.     

Synthesis of Nitrogen‐Containing Rubicene and Tetrabenzopentacene Derivatives

Carbon‐based materials, such as acenes, fullerenes, and graphene nanoribbons, are viewed as the potential successors to silicon in the next generation of electronics. Although a number of methodologies provide access to these materials’ all‐carbon variants, relatively fewer strategies readily furnish their nitrogen‐doped analogues. Herein, we report the rational design, preparation, and characterization of nitrogen‐containing rubicenes and tetrabenzopentacenes, which can be viewed either as acene derivatives or as molecular fragments of fullerenes and graphene nanoribbons. The reported findings may prove valuable for the development of electron transporting organic semiconductors and for the eventual construction of larger carbonaceous systems.     

Eigenvalues of ‐Free Graphs and the Connectivity of Their Independence Complexes

Let G be a graph on n vertices, with maximal degree d, and not containing as an induced subgraph. We prove:

• 1.
• 2.

Here is the maximal eigenvalue of the Laplacian of G, is the independence complex of G, and denotes the topological connectivity of a complex plus 2. These results provide improved bounds for the existence of independent transversals in ‐free graphs.     

Large sets in finite fields are sumsets

For a prime p, a subset S of Zp is a sumset if S=A+A for some A⊂Zp. Let f(p) denote the maximum integer so that every subset S⊂Zp of size at least p−f(p) is a sumset. The question of determining or estimating f(p) was raised by Green. He showed that for all sufficiently large p, and proved, with Gowers, that f(p)<cp2/3log1/3p for some absolute constant c. Here we improve these estimates, showing that there are two absolute positive constants c₁,c₂ so that for all sufficiently large p,

     

Tail expansions for the distribution of the maximum of a random walk with negative drift and regularly varying increments

Let F$F$ be a distribution function with negative mean and regularly varying right tail. Under a mild smoothness condition we derive higher order asymptotic expansions for the tail distribution of the maxima of the random walk generated by F$F$. The expansion is based on an expansion for the right Wiener–Hopf factor which we derive first. An application to ruin probabilities is developed.     

Degrees and choice numbers

The choice number ch(G) of a graph G=(V, E) is the minimum number k such that for every assignment of a list S(v) of at least k colors to each vertex v∈V, there is a proper vertex coloring of G assigning to each vertex v a color from its list S(v). We prove that if the minimum degree of G is d, then its choice number is at least (½−o(1))log₂ d, where the o(1)‐term tends to zero as d tends to infinity. This is tight up to a constant factor of 2+o(1), improves an estimate established by the author, and settles a problem raised by him and Krivelevich. © 2000 John Wiley & Sons, Inc. Random Struct. Alg., 16, 364–368, 2000