Reactivity of an o-indoloquinone to 1- and 2-azadienes

The cycloaddition reactions of o-indoloquinone 4 to azadienes are described. With 1-azadiene 2, quinone 4 works as a dienophile to give the directly aromatized cycloadduct 6. In contrast, when 2-azadiene 3 is used, the cycloaddition occurs with CO-4, indicating that this system functions as a heterodienophile.     

Norbornene probes for the study of cysteine oxidation

Cysteine residues on proteins can react with cellular oxidants such as hydrogen peroxide. While this process is important for scavenging excess reactive oxygen species, the products of this oxidation may also mediate cell signalling. To understand the role of cysteine oxidation in biology, selective probes are required to detect and quantify its occurrence. Cysteine oxidation products such as sulfenic acids are sometimes unstable and therefore short-lived. If such cysteine derivatives are to be analysed, rapid reaction with the probe is required. Here we introduce norbornene derivatives as probes for cysteine oxidation, and demonstrate their ability to trap sulfenic acids. The synthesis of norbornene derivatives containing alkyne or biotin affinity tags are also reported to facilitate the use of these probes in chemical biology and proteomics.     

How Fast can a Subharmonic Function Decay Along a Ray?

Much is known about the connection between the growth and decayof subharmonic functions. The results indicate that there isa general principle: asubharmonic function cannot decay ‘toofast’ relative to its growth.Three theorems are provedwhich, together with work previously published elsewhere, givea fairly complete account of how this principle works out fora subharmonic function having extremal decay along a ray. 1991Mathematics Subject Classification: 30D20, 31A05.     

A Minimal,Unstrained S‐Allyl Handle for Pre‐Targeting Diels–Alder Bioorthogonal Labeling in Live Cells

The unstrained S‐allyl cysteine amino acid was site‐specifically installed on apoptosis protein biomarkers and was further used as a chemical handle and ligation partner for 1,2,4,5‐tetrazines by means of an inverse‐electron‐demand Diels–Alder reaction. We demonstrate the utility of this minimal handle for the efficient labeling of apoptotic cells using a fluorogenic tetrazine dye in a pre‐targeting approach. The small size, easy chemical installation, and selective reactivity of the S‐allyl handle towards tetrazines should be readily extendable to other proteins and biomolecules, which could facilitate their labeling within live cells.     

On the set of points with a dense orbit

Under certain conditions on the topological space we prove that for every continuous map the set of all points with a dense orbit has empty interior in . This result implies a negative answer to two problems proposed by M. Barge and J. Kennedy.

     

Qualitative properties of modified equations

Suppose that a consistent one-step numerical method of orderr is applied to a smooth system of ordinary differential equations.Given any integer m 1, the method may be shown to be of orderr + m as an approximation to a certain modified equation. Ifthe method and the system have a particular qualitative propertythen it is important to determine whether the modified equationsinherit this property. In this article, a technique is introducedfor proving that the modified equations inherit qualitativeproperties from the method and the underlying system. The techniqueuses a straightforward contradiction argument applicable toarbitrary one-step methods and does not rely on the detailedstructure of associated power series expansions. Hence the conclusionsapply, but are not restricted, to the case of Runge-Kutte methods.The new approach unifies and extends results of this type thathave been derived by other means: results are presented forintegral preservation, reversibility, inheritance of fixed points.Hamiltonian problems and volume preservation. The techniquealso applies when the system has an integral that the methodpreserves not exactly, but to order greater than r. Finally,a negative result is obtained by considering a gradient systemand gradient numerical method possessing a global property thatis not shared by the associated modified equations.     

Allyl sulfides are privileged substrates in aqueous cross-metathesis: application to site-selective protein modification

Allyl sulfides undergo efficient cross-metathesis in aqueous media with Hoveyda-Grubbs second generation catalyst 1. The high reactivity of allyl sulfides in cross-metathesis was exploited in the first examples of cross-metathesis on a protein surface. S-Allylcysteine was incorporated chemically into the protein, providing the requisite allyl sulfide handle. Preliminary efforts to genetically incorporate S-allylcysteine into proteins are also reported.