Max Flow and Min Cut with bounded-length paths: complexity, algorithms, and approximation

We consider the “flow on paths” versions of Max Flow and Min Cut when we restrict to paths having at most B arcs, and for versions where we allow fractional solutions or require integral solutions. We show that the continuous versions are polynomial even if B is part of the input, but that the integral versions are polynomial only when B ≤ 3. However, when B ≤ 3 we show how to solve the problems using ordinary Max Flow/Min Cut. We also give tight bounds on the integrality gaps between the integral and continuous objective values for both problems, and between the continuous objective values for the bounded-length paths version and the version allowing all paths. We give a primal–dual approximation algorithm for both problems whose approximation ratio attains the integrality gap, thereby showing that it is the best possible primal–dual approximation algorithm.     

High-performance liquid chromatography of biotin and analogues

Biotin, analogues, and chemical intermediates were separated by high-performance liquid chromatography (HPLC) using reversed-phase and anion-exchange chromatographic conditions. Reversed-phase separations provided a wide range of retention times and resolution of nearly all the biotin compounds from mixtures of the analogues. Anion-exchange separations gave generally shorter retention times as compared to reversed-phase separations and greater resolution between biotin l- and d-sulfoxide. However, fewer analogues were resolved from mixtures of the compounds with anion-exchange HPLC.     

Site‐Specific Encoding of Photoactivity in Antibodies Enables Light‐Mediated Antibody–Antigen Binding on Live Cells

Antibodies have found applications in several fields, including, medicine, diagnostics, and nanotechnology, yet methods to modulate antibody–antigen binding using an external agent remain limited. Here, we have developed photoactive antibody fragments by genetic site‐specific replacement of single tyrosine residues with photocaged tyrosine, in an antibody fragment, 7D12. A simple and robust assay is adopted to evaluate the light‐mediated binding of 7D12 mutants to its target, epidermal growth factor receptor (EGFR), on the surface of cancer cells. Presence of photocaged tyrosine reduces 7D12‐EGFR binding affinity by over 20‐fold in two out of three 7D12 mutants studied, and binding is restored upon exposure to 365 nm light. Molecular dynamics simulations explain the difference in effect of photocaging on 7D12‐EGFR interaction among the mutants. Finally, we demonstrate the application of photoactive antibodies in delivering fluorophores to EGFR‐positive live cancer cells in a light‐dependent manner.     

Quark-hadron duality in neutron (3He) spin structure

We present experimental results of the first high-precision test of quark-hadron duality in the spin-structure function g_{1} of the neutron and 3He using a polarized 3He target in the four-momentum-transfer-squared range from 0.7 to 4.0 (GeV/c);{2}. Global duality is observed for the spin-structure function g_{1} down to at least Q;{2}=1.8 (GeV/c);{2} in both targets. We have also formed the photon-nucleon asymmetry A1 in the resonance region for 3He and found no strong Q2 dependence above 2.2 (GeV/c);{2}.     

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.     

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.     

Ambient-temperature metal-to-ligand charge-transfer phosphorescence facilitated by triarylboron: Bnpa and its metal complexes

A Cu(I) complex, 1, and a Pt(II) complex, 2a, of a triarylboron ligand, Bnpa, with bright ambient-temperature phosphorescence have been obtained. The phosphorescence of these complexes is highly sensitive toward molecular oxygen and has a distinct response to fluoride ions. For 1, the fluoride ion causes phosphorescent quenching and Bnpa dissociation, and for 2a, it switches phosphorescent color from yellow to green. The Cu(I) complex has an exceptionally high emission quantum yield (0.88) in the solid state.     

Copper and iron interactions with angiotensin-converting enzyme inhibitors. A study by fast-atom bombardment tandem mass spectrometry

Fast atom bombardment, combined with high-energy collision-induced tandem mass spectrometry, has been used to investigate gas-phase metal-ion interactions with captopril, enalaprilat and lisinopril, all angiotensin-converting enzyme inhibitors.Suggestions for the location of metal-binding sites are presented. For captopril, metal binding occurs most likely at both the sulphur and the nitrogen atom. For enalaprilat and lisinopril, binding preferably occurs at the amine nitrogen. Copyright 1999 John Wiley & Sons, Ltd.