A Bioorthogonal Small‐Molecule‐Switch System for Controlling Protein Function in Live Cells

Chemically induced dimerization (CID) has proven to be a powerful tool for modulating protein interactions. However, the traditional dimerizer rapamycin has limitations in certain in vivo applications because of its slow reversibility and its affinity for endogenous proteins. Described herein is a bioorthogonal system for rapidly reversible CID. A novel dimerizer with synthetic ligand of FKBP′ (SLF′) linked to trimethoprim (TMP). The SLF′ moiety binds to the F36V mutant of FK506‐binding protein (FKBP) and the TMP moiety binds to E. coli dihydrofolate reductase (eDHFR). SLF′‐TMP‐induced heterodimerization of FKBP(F36V) and eDHFR with a dissociation constant of 0.12 μM . Addition of TMP alone was sufficient to rapidly disrupt this heterodimerization. Two examples are presented to demonstrate that this system is an invaluable tool, which can be widely used to rapidly and reversibly control protein function in vivo.     

Topological mixing in -spaces

If is a proper -space and a non-elementary discrete group of isometries acting properly discontinuously on it is shown that the geodesic flow on the quotient space is topologically mixing, provided that the generalized Busemann function has zeros on the boundary and the non-wandering set of the flow equals the whole quotient space of geodesics (the latter being redundant when is compact). Applications include the proof of topological mixing for (A) compact negatively curved polyhedra, (B) compact quotients of proper geodesically complete -spaces by a one-ended group of isometries and (C) finite -dimensional ideal polyhedra.

     

Approximationstheorie für metrische lineare Räume

Ohne Zusammenfassung     

A general method for the synthesis of bastaranes and isobastaranes: first total synthesis of bastadins 5, 10, 12, 16, 20, and 21

A general strategy for the synthesis of twenty naturally occurring bastadins (all but bastadin 3) is presented. A key retrosynthetic disconnection of the two amide bonds, common in all target molecules, bisects the macrocyclic core into two diaryl ether fragments, an alpha,omega-diamine (western part) and an alpha,omega-dicarboxylic acid (eastern part). Efficient preparation of the synthetically challenging o-mono or dibromo-substituted diaryl ether linkages was achieved employing the diaryl iodonium salt method. Regarding the western part, variations of the aliphatic chain were more efficiently secured by the preparation of two different alpha,omega-aminonitrile moieties. Cobalt boride mediated reduction of the nitrile functionality established the required diamines and, at the same time, provided the necessary variation of the aromatic-ring bromination pattern. Regarding the eastern part, two different dicarboxyl precursors had to be prepared in order to accommodate bromination-pattern variations. Coupling and subsequent macrolactamization of different combinations of these key intermediates may lead at will to any member of this family of marine natural products. Four bastaranes (bastadins 5, 10, 12 and 16) and two isobastaranes (bastadins 20 and 21) were synthesized as a demonstration of the flexibility and efficiency of the approach presented.     

Intramolecular and intermolecular kinetic isotope effects (KIE) in the nitrosoarene ene reaction: experimental evidence for reversible intermediate formation

The intramolecular and intermolecular kinetic isotope effects (KIE) have been determined for the nitrosoarene ene reaction with deuterium-stereolabeled 2,3-dimethyl-2-butenes (TME). trans-TME-d(6) (k(H)/k(D) = 3.0) and gem-TME-d(6) (k(H)/k(D) = 4.0) show large intramolecular primary isotope effects. In contrast, the intramolecular competition in cis-TME-d(6) (k(H)/k(D) = 1.5) and the intermolecular competition for the TME-d(0)/TME-d(12) pair (k(H)/k(D) = 1.98) show considerably smaller, but mechanistically significant kinetic isotope effects. The latter fact is rationalized in terms of reversible formation of a three-membered-ring intermediate, namely the aziridine N-oxide, or a similar unsymmetrical, polarized diradical in the first step of the reaction. Such reversibility has also been implied earlier for triazolinedione (TAD) and singlet oxygen ((1)O(2)) with deuterium-stereolabeled 2-butenes, but of the three enophiles, ArNO is the most sensitive toward reversibility, which is due to its moderate reactivity and its high steric demand.     

Labeling of organic biomolecules with ethynylferrocene

The Sonogashira coupling reaction of ethynylferrocene with adenine, uracil, tyrosine and steroid derivatives was studied; with the exception of tyrosine it was proved to be a good route for the attachment of ferrocene to these representative biomolecules. In addition the transformation of alkynyl uracil to furanopyrimidone derivatives was investigated and the formation of the furanopyrimidone ring was confirmed by an X-ray crystallographic analysis carried out on product 16.     

A variational principle for adaptive approximation of ordinary differential equations

Summary A variational principle, inspired by optimal control, yields a simple derivation of an error representation, global error=local errorweight, for general approximation of functions of solutions to ordinary differential equations. This error representation is then approximated by a sum of computable error indicators, to obtain a useful global error indicator for adaptive mesh refinements. A uniqueness formulation is provided for desirable error representations of adaptive algorithms. Mathematics Subject Classification (2000):65L70, 65G50This work has been supported by the EU–TMR project HCL # ERBFMRXCT960033, the EU–TMR grant # ERBFMRX-CT98-0234 (Viscosity Solutions and their Applications), the Swedish Science Foundation, UdelaR and UdeM in Uruguay, the Swedish Network for Applied Mathematics, the Parallel and Scientific Computing Institute (PSCI) and the Swedish National Board for Industrial and Technical Development (NUTEK).     

On the large time behavior of the heat kernels of quasiperiodic differential operators

We prove an analog of the Berry-Esseen estimate for the heat kernel of second order elliptic differential operators with quasiperiodic coefficients. As an application of this result, we prove the L^p boundedness of the associated Riesz transform operators.